He doesn't need it in order to breathe and stay alive *per se* (in the film) but to administer inhaled anesthetics in order to ease the pain left from old injuries suffered at The Pit (mainly to his face I'm guessing?)

The fact that he has to permanently wear it and quickly gets incapacitated the moment that Batman detaches a few tubes (punching him a couple of times during the final fight) proves that...

A) The pain truly is exorbitantly high.

B) Bane has a very low pain-tolerance curve in the afflicted areas of his body (again the face) which usually happens to scarred tissues and surroundings.

AND / OR

C) Bane has developed a severe case of drug dependency over two decades years of slow periodic administration, which means he will need to use larger doses as time goes in order to feel better and the slightest interruption of said dosage will cause the pain to spike and hit him hard.

I'ma bet it's a combination of all three aspects (mainly the last one) as to why the mask is so important to him in the movie.

What I'm truly curious, though, is as to what exactly does he receive that eases his pain **without** compromising his awareness and conscious status xD