Try out a couple of brands. Some last better than others. Only wash as necessary. This really depends on how you sweat and what sort of activities you do: If you aren't all that sweaty, you can probably get at least 2-3 days out of each. Wear an apron while cooking and other sorts of things to keep it clean a bit longer.

Don't let your cat knead your stomach with her claws: You'll eventually find little holes. That might just be me, though :)

Granted, all of this might not get you all that far, but is worth a shot. I generally have fewer shirts than you that last at least a year (some are long sleeve, some short, all black).

Buy Carhartt. They make their clothing to last. Heavier materials, better stitching. You'll be lucky to wear one out in 3 years.

Use some as cleaning cloths.