As I mentioned in the comments, you're looking at the wrong aspect of armor. You shouldn't be looking at the percentage it reduces, but rather the amount of damage it actually prevents as a measure of how much longer that armor lets your survive.
Let's consider an example for a champion with 0 armor. Say he has 1000 health, just 'cause that's a nice round number. Now our champion gets caught in Garen's judgement, and starts taking 100 physical damage each second (at one hit per second). Clearly, our protagonist can take ten hits before dying.
But now, imagine our champion has the 50 armor you mention, meaning the incoming physical damage is reduced. Now (still with 1000 health) it takes 15 seconds for that bastard Garen to claim our champion's life. 50 armor extended our life by 5 seconds. (100 * (2/3) = 66.6 DPS; 1000 / 66.66... = 15 hits)
So our champion respawns, wises up, and buys 50 more armor. Now with 100 armor, we're sitting at a flat 50% damage reduction. Again we run into Garen, who's still dealing 100 base damage per second. It now takes him twice as long to kill us -- 20 seconds. Once again the armor has extended our life, again by 5 seconds. (100 * .5 = 50 DPS; 1000 / 50 = 20 hits)
Back in base, we buy another 50 armor. We're now at 150 armor, and 60% damage reduction. Enter Garen -- spinspinspinspinspinspin and it takes 25 seconds before our champion dies. Again, adding 50 armor extended our life by 5 seconds. (100 * .4 = 40 DPS; 1000 / 40 = 25 hits)
So even while the amount of damage reduced per point of armor diminishes (as you observed), the amount of time armor extends your life (or effective health) remains distinctly linear.
I suspect that your 71 HP "Healing" was a result of killing 2-3 neutral creep camp leaders while hurt over the course of the game and receiving the minor heal they now give on death as part of the jungle revamp. The tally shows you as killing 34 Neutral creeps. If you killed about 1/3 of them when you were hurt (so that the heal would have an effect) that comes out to around 71 HP.
Best Answer
Countering damage over time, like any other damage, depends on largely what kind of damage you are taking. If, for example, you are being hurt by Teemo's Toxic Shot, then you'll want to get items with magic resist. If Talon's Noxian Diplomacy is your bane, then you'll want to build more armor. Health is also a solid option if you have problems with both and you'll want to build some health anyways to enhance the effects of increased armor and/or magic resistance.
Unfortunately, building more magic resist or armor will not help against Twitch's damage over time. Twitch's Deadly Venom deals true damage, which ignores all damage reduction from armor and magic resistance. Therefore, your only option is to build more health.
Your other option is find a way to remove the damage-over-time effect, which can only be achieved through the Quicksilver Sash or its upgrade, the Mercurial Scimitar. While the summoner spell Cleanse can clear crowd control debuffs, it will not remove most damage-over-time effects as they are typically not tied to crowd control effects.