keyword: breathing exercises (google breathing exercise singing). Because how fast you run out of air doesn't only depend on how much lung volume you have, but also on how slowly you breathe out, and how efficiently you use your air.
um, iunderstand. im beggining to have same problem, which is sad, cause i just relearned how to sing due to voice changing pitch. i get around my problem by practicing a lot. dunno if that helps, but i tried.