Rules as written: No limit

Armors limit your Dex bonus to AC. Deepwardens do not have Dex bonuses to AC, they have Con bonuses to AC. The Con bonus replaces the Dex bonus (and so you would not get it in situations where you lose your Dex bonus to AC), but it still is not a Dex bonus and thus the limits of the armor do not apply. And, indeed, there’s no reason why an armor’s weight or inflexibility would prevent you from benefiting from your resilience and connection to the earth.

Intent: Unknown, and unknowable

As far as what the authors intended, that’s anyone’s guess. The author never wrote anything on the subject aside from the original publication, so we have no evidence one way or the other.

Precedent: No limit

As for precedence, generally speaking the special rules for one ability score do not apply when you swap to another ability score. There are instances where you can replace your Strength to damage with Dexterity to damage, but RAW you do not get ½Dexterity to damage on a light weapon or 1½Dexterity to damage on a weapon wielded two-handed, unless it explicitly says so. (Dragon vol. 221 has the Corsair which explicitly halves Dexterity to damage with light weapons, for example)

FAQ: Limit

However, there is an FAQ entry on the question. The FAQ, it must be very clearly stated, is not errata. It is supposed to only explain the rules that already exist. If its statements contradict the actual rules, officially, the actual rules take precedence every single time. And the FAQ has been wrong many times, in many cases quite blatantly so. Finally, the FAQ is not (usually) written by the original authors of the book, so it does not correspond to the author’s intent, either.

All together, the FAQ is worth very little, and has a very poor reputation. In fact, it’s so bad that when this poster in the thread Squera linked learned that the FAQ said the Con bonus was limited, it proved to him that it actually wasn’t!

At any rate, the FAQ has this to say:

Does the deepwarden’s Stone Warden ability (RS 105) still have a maximum Dexterity bonus to his Armor Class, and does that maximum still apply to his Constitution?

The maximum Dexterity bonus should be treated as the maximum ability bonus given by the armor, so if you were playing a deepwarden wearing full plate, you would only add 1 to your Armor Class from your Constitution.

Conclusion: Rule it based on what improves your game most

Personally, I think it makes almost no sense that restrictive armor would inhibit a Con bonus to AC, I think that deepwardens make sense in heavy armor and shouldn’t be penalized for wearing it, and I don’t think the deepwarden or the AC they can get is overpowered or problematic, so I would not limit it. You may answer any or all of those questions differently. Ultimately, remember than AC is a limited thing, and lots of nasty things ignore AC; having a lot of it only does so much for you.

If you would like a compromise, here’s a suggestion. Purely houserule with no basis in the rules, either deepwarden’s or elsewhere in precedence, but it might be a good solution:

The deepwarden’s Constitution bonus to AC is limited by her armor’s maximum Dexterity bonus, just as the Dexterity bonus it replaces would be. However, the Constitution bonus is not limited for the purposes of AC against touch attacks. For example, if a deepwarden with 18 Constitution (+4) wears Chainmail (+5 AC, +2 maximum Dexterity bonus), and has no other bonuses to AC, his AC is 17 (+5 armor, +2 Consitution), but his touch AC is 14 (+4 Constitution). A deepwarden’s touch AC may not exceed her regular AC.

I don’t think this is necessary, but it does prevent the high-end AC that you might get from armor+Con, while still giving a deepwarden a good bonus for their class feature.

Remember, a class feature is supposed to make you better. Yes, Con, not limited by max Dex, is better than what the deepwarden had before, but that isn’t necessarily a problem. It’s only a problem if it’s “too much better,” and I really don’t think it is.

Questions and Answers

• Question: When the Handle Animal skill is used for the task Rear Wild Animal, what's the Handle Animal skill check's DC?

  Answer: The base DC is 15 plus the number of HD the creature possesses. The trainer spends 3 hours each day with the creature and, halfway through the task Rear Wild Animal, makes the Handle Animal skill check. Success means the animal is successfully reared if the trainer completes the required time with the creature, while failure means no further time need be spent and the creature remains undomesticated. The task Rear Wild Animal cannot be retried.

  Example 1: To perform the Rear a Wild Animal task on the typical dodo the trainer makes a Handle Animal skill check (DC 16).

  Example 2: To perform the Rear a Wild Animal task on the typical owlbear the trainer makes a Handle Animal skill check (DC 25). The task's DC is increased by 5 because the owlbear is a magical beast. (But see below.)

  Example 3: To perform the Rear a Wild Animal task on the typical blue whale the trainer makes a Handle Animal skill check (DC 31).

• Q: How long does the task Rear an Animal take to complete?

  A: The DM must determine this. A reasonable house rule might be that the skill Handle Animal be used like the skill Profession. That is, treat the training cost as if the trainer were using the skill Handle Animal instead of the Profession skill to earn the cost in gp of the rearing. Thus if a creature has a cost associated with its rearing but gives no indication of how long that rearing takes, divide twice that cost by the check's DC and this is the number of weeks it takes the trainer to perform the Rear an Animal task. This equation can be used to determine cost instead if time's provided.

  Example 1: "Professional animal trainers charge up to 2,000 gp to rear or train an owlbear into a serviceable guardian that can obey simple commands (DC 23 for a juvenile creature; DC 30 for a fully grown adult)." (2,000 gp x 2) / DC 23 = 173.9 weeks, or over 3 years for a juvenile owlbear. Note: The parenthetic differs from the Handle Animal skill's details--the first DC is too low, the second task impossible. Exceptions win.

  Example 2: "Taming a trollhound requires 4 weeks of work and a DC 25 Handle Animal check." 2 x 4 weeks x DC 25 = 200 gp.

  Example 3: "It takes 3 years for a hieracosphinx to reach maturity...." 2 x 156 weeks x DC 28 = 8,736 gp. Note: According to the text, "Trainers [are] hard to come by [and] charge thousands of gold pieces to rear and train a hieracosphinx, owing to the risk to life and limb." Indeed, and that's despite the hieracosphinx having an Intelligence score of 6 and speaking the language Sphinx.

  Many creatures' entries that contain details about the theft of their eggs or young (e.g. the amphisbaena, the hippogriff, the pegasus, the roc) lack subsequent details about rearing those creatures. The DM could, however, house rule that value into also equaling the additional cost for rearing the animal, allowing the DM to determine rearing times for those animals as well. This will have the hilarious result of cheap animals being reared extremely quickly though, which might be a concern, but it can be a starting point.