01 Chevy Tahoe, Only starts when it wants to

Every once in a while (about once a day) my SUV won't start. I have a fairly new battery and have not had any power loss once so ever. The starter engages and the vehicle turns over but within 1 second it dies off. I've checked all fuses and all spark plugs. Everything seems to be connected. After waiting aprx. 10-15 min the vehicle starts up without a problem. No warning lights on the display. It sounds to be running perfectly fine. I have taken it to a mechanic and it started for him 2 dozen times without a problem. It doesn't matter if the vehicle sits for 12 hours or 5 minutes. It has a mind of its own.