Oxygen molecules would be bigger than him, and they therefore wouldn't be able to fit into his tiny lungs to have oxygen available for cellular respiration, and thence the energy to live. He was at a sub-atomic size for quite a while, and I'm not sure that the suit supplies him with oxygen. An atom is mainly empty space...
What really sparked my interest is when Hank Pym (in the end) thinks that his wife could still be alive - it is plausible that since physics at the sub-atomic level is different than how we experience it in every day life. But for her, time will be passing at the same rate as normal. If Pym could find her, his time experience would be different, and she would experience a long time at sub-atomic size with her oxygen levels probably depleted (present only minimally in small air spaces in her suit), and would suffocate.
How is what Pym believes justifiable, and how could Ant Man have spent so long in a sub-atomic state and still be alive ?