I have 2004 Maxima SL and if the car is driven or idle for about 10 or 15 minutes and you stop and shut it off it will not restart. When the car is running it run great.

 

Any CEL's? Sounds like you need to check for spark and if you can listen with an automotive stethoscope to ensure your injectors are actuating and your fuel pump is working! You might be having a cam sensor/crank sensor issue! Also might sure the Crankshaft sensor is clean and not full of metal shavings.