Contextually, Bob's correct
If the campaign is a series of tombs of horrors, then that ring of cure light wounds is an item beyond price. If the party can't leave the dungeon to resupply and can't get down to one encounter per day (i.e. the so-called 15-minute workday) via spells1, that ring of cure light wounds is a literal lifesaver.
In other words, if the campaign is already on hard mode, the ring switches it not to easy mode, certainly, but to average mode. That's a legitimate concern for the DM. The DM's already decided the campaign's supposed to be difficult and the ring makes the campaign substantially less difficult. As the ring violates a central campaign tenet, the ring just shouldn't be available… or only available as a result of a heinous Gygaxian Faustian bargain.
For the game as it was likely envisioned, Erin's correct
The Dungeon Master's Guide would likely pick Erin's suggestion. If worry-free, constant healing is desired, everybody should pony up for rings of regeneration (DMG 232) (90,000 gp; 0 lbs.). Sure, each ring of regeneration costs as much as 120 wands of cure light wounds [conj] (PH 215–16) (1st-level spell at caster level 1) (15 gp/charge), but, y'know, the Dungeon Master's Guide says to "[u]se good sense when assigning prices, using the items in this book as examples" (282), and the ring of regeneration presents the example of the price of worry-free, constant healing, so that is the price of worry-free healing. In fact, an original magic item like a use-activated ring of cure light wounds—like a continuous item of true strike [div] (PH 296)—is such an anathema, I'm willing to bet were the year 2000 Dungeon Master's Guide a DM that it would laugh at the player who suggested a ring of cure light wounds and maybe have the next wandering monster attack him first just for asking.
For many games as they are now, Alice or Dave is correct
Many current players feel that constantly reacquiring wands of cure light wounds to have their characters freshen up between encounters is, at worst, a mere inconvenience, like tracking how many arrows remain in a quiver. In the same way that being short on arrows creates tension at low levels, managing healing resources at low levels creates tension. Many players, though, feel that by the time a character's reached a reasonably high level—say, 9 or so—that the character should have more important things to worry about than how many arrows he has left, and he shouldn't worry that he's burning party resources because he fell down a 200-ft.-deep pit. A Ftr9's Wealth by Level (Dungeon Master's Guide (203) 135) says that a wand of cure light wounds—that is, an entire wand, fully charged—is only about 2% of the gear he's toting. Seriously, after splitting four ways the take from a lone level-appropriate encounter, a Ftr9 can buy a whole new fresh wand of cure light wounds and still have gp left over.
If a DM has players like Alice and Dave, a ring of cure light wounds makes the game more fun because it cuts down on tracking charges from wands of cure light wounds, and the DM should probably allow it—either at low levels at Alice's price or higher levels at Dave's price—unless the DM's vision of the game differs substantially from that of the players' vision.
A brief history of the ring of regeneration
As the sole item that grants continuous healing in core Dungeons and Dragons 3.5, the ring of regeneration is terrible and using it as an example of what continuous healing should cost is terrible. I'll explain.
Building as they were in 2000 from Advanced Dungeons and Dragons, 2nd Edition, the ring of regeneration included in the Dungeon Master's Guide for Dungeons and Dragons, Third Edition probably looked fine to the original core rules' authors. The changes made to the ring of regeneration were a much needed nerf to improvement over Advanced Dungeons and Dragons, 2nd Edition's ring of regeneration, which, for the record,
restores 1 point of damage each turn [10 minutes] and eventually replaces lost limbs and organs. It will bring its wearer back from death…. Only total destruction of all living tissue by fire, acid, or similar means will prevent regeneration. Of course, the ring must be worn, and its removal stops the regeneration process.2 (Encyclopedia Magica, Vol. 3 993)
Such an item was highly coveted in both Advanced Dungeons and Dragons (where it functioned similarly) and Advanced Dungeons and Dragons, 2nd Edition, and for good reason. One's character could lose limbs and organs. ("Why, hello there, sword of sharpness!") Dying was really painful instead of the speed bump that it typically is in Dungeons & Dragons, Third Edition. And healing was, itself, extremely valuable, the province of classes that often weren't much fun to play and rarely advanced beyond level 6 through actual play.3
So when the time came to include the highly-sought-after ring of regeneration in Dungeons and Dragons, Third Edition, the price was set very high because legacy yet the ring's actual functionality plummeted. Creatures no longer lost limbs except under extremely rare circumstances. Creatures now healed their levels or HD in hp per 8 hours rest instead of just 1 point per day of rest. And gone was the jazz about the ring bringing the wearer back from the dead. The only improvement Dungeons and Dragons, Third Edition made to the ring was proportionate healing (that is, Third Edition's heals a creature's level in hp)… and then Third Edition multiplied the ring's healing increment by 6.
Anyway, the current ring of regeneration seriously sucks as useful measure by which to gauge unlimited healing.
1 By, after the first encounter, hiding in, for example, the space created by the 2nd-level Sor/Wiz spell rope trick [trans] (Player's Handbook 273), the 5th-level initiate of Gruumsh (CR 24) spell pocket cave [conj] (Champions of Ruin 33), or the 7th-level Sor/Wiz spell Mordenkainen's magnificent mansion [conj] (PH 256).
2 Okay, a similar means to fire is heat. Sure. I get that. That's a thing. But what's a similar means to acid except, like, better acid? I hope whoever wrote that spent his $0.10 from those words wisely.
3 I find the experience level chart for the cleric or priest, respectively, in Advanced Dungeons and Dragons or Advanced Dungeons and Dragons, 2nd Edition—when compared to classes' experience level charts—hilarious.
You're misusing the guidelines.
First, let's take a look at what the Pathfinder Magic Item Gold Piece Values section has to say on this issue. Turns out, it is specifically addressed.
The correct way to price an item is by comparing its abilities to similar items (see Magic Item Gold Piece Values), and only if there are no similar items should you use the pricing formulas to determine an approximate price for the item. If you discover a loophole that allows an item to have an ability for a much lower price than is given for a comparable item, the GM should require using the price of the item, as that is the standard cost for such an effect. Most of these loopholes stem from trying to get unlimited uses per day of a spell effect from the "command word" or "use-activated or continuous" lines of Table: Estimating Magic Item Gold Piece Values.
Emphasis mine. It then goes on to take Mage Armor as an example of this:
Patrick's wizard wants to create bracers with a continuous mage armor ability, granting the wearer a +4 armor bonus to AC. The formula indicates this would cost 2,000 gp (spell level 1, caster level 1). Jessica reminds him that bracers of armor +4 are priced at 16,000 gp and Patrick's bracers should have that price as well. Patrick agrees, and because he only has 2,000 gp to spend, he decides to spend 1,000 gp of that to craft bracers of armor +1 using the standard bracer prices.
So yes, your Amulet of Mage Armor and Shield is a textbook example of the guidelines gone bad.
This is understandable. The guidelines are famously weak, often breaking with casual use, as you have encountered. This precise case, however, was anticipated and addressed.
Best Answer
The Magic Item Creation rules are guidelines.
The most important thing to remember when making magic items in Pathfinder is that the rules for making items are guidelines, not hard-and-fast rules. Making new magic items is a very subjective process, and no set of rules is going to give you balanced items each time. The only way to reliably price new magic items is to make new magic items and price them, and see how effective they are in play. Experience is much more important than rules, here.
The base price for command word or use-activated items is for at-will use.
Command-word and use-activated items are, by default, usable as many times per day as you want. There is no limit to the number of times you can use that kind of item in a day.
As an example, the Hand of the Mage. It lets you use mage hand as a standard action, as much as you'd like. It costs 900 gp, which is spell level (.5) times caster level (1) times the command-word constant (1800) for an even 900 gp.
Very few command-word items exist that don't have a per-day limit to their use, because at-will usage of many effects is significantly more powerful than just being able to use it once per day.
Always check for similar effects when pricing at item.
This is the second most important rule of magic item creation. A large number of effects are already represented in the existing magic item rules. If the item that you want to make duplicates the effect of an existing item, then it should cost the same as the existing item.
For your example of an item that lets you cast mage armor you should compare it to existing items that do the same effect, like the Bracers of Armor. The +4 Bracers give you a +4 armor bonus to AC all day long, with no activation needed, and cost 16,000 gp. Your item gives you a +4 armor bonus to AC for 3 hours a day, and needs an activation before it can be used. Clearly, your item should cost less, but exactly how much less is something that's more left to how the DM feels about the item's cost than any hard rule. Personally, I'd go with around 8,000 gp. If you're having about 4 encounters a day, and you have the ability to more-or-less predict half of them, then you're getting about half the benefit that the Bracers of Armor +4 would give you, so I'd charge about half for the item. But that's just how I would run it, and it's more important that you price it in a way that makes sense to you.