Before I broke my leg, I was riding about 20-30 miles a week. and I"m a BIG guy, 350+ pounds. I was riding either my Specialized Hardrock with stock wheels, my Redline hybrid with Alex 298 rims, or my 85 Schwinn Traveler with stock 36 spoke 27 1/4 inch wheels and never broke a spoke once.
The Trek should have good wheels. Are you doing anything like bunny hopping, jumping off curbs, etc? Seems like you are breaking an inordinate amount of spokes.