Got enough LP in your soul network? The bound armor will literally eat you up if it runs out of LP to fuel its demonic protection ability. And if you slotted lots of sigils with passive upkeep costs, your LP may drop faster than you think.
You don't need bound armor to survive there either. I never built more than the chestplate the relevant quest required me to, and I did fine with the rest of the slots occupied by glowstone or steel armor pieces (looted faster than I could ever use them up from my constant and numerous mob sacrifices) and a glowstone sword. Unenchanted stuff, even. Granted, I did slot a lava sigil and a master orb into the bound chestplate, for unlimited free fire immunity. That's kind of required in that nether fortress. If you go there without fire immunity, you will die. Even if you don't die to the fire, it will keep your health down so that something else will kill you.
High-grade golden apples also give you fire immunity, so if you didn't slot it into your bound armor, those are a good backup. They also give you regeneration, which makes for significantly less dying. Considering this map throws excessive amounts of high-grade golden apples at you in every second quest, I think you should have the ability to be a bit wasteful and just use them to keep the buffs up permanently while you're in the fortress.
Another very much life preserving measure is disabling hostile mob spawns... in other words, light that sucker up. Torches everywhere. Press F7 to let NEI show you where there is not enough light yet, and remove blaze fires to make sure you aren't deceived. Blazes and zombie pigmen will still spawn anyway, but the latter shouldn't bother you if you don't bother them, and against the former you should be immune. Especially light up all the side paths, so you create an area where you're guaranteed to be free from hostile monsters (aside from ineffectual blazes). If you only light up the main path you follow, skeletons will keep pouring in from the sides and block your retreat. Prepare to spend 2-3 stacks of torches on this.