Is the theft light flashing when this happens?
Do you hear the fuel pump run when it will not start?
If you hold down on the gas pedal slightly will it start?
Well, there are a couple of more common issues you can check:
1) There is a ground (G104) located below the battery tray that may be corroded. It would cause the complaint you are describing. You will need to remove and clean the ground even if it looks good.
2) The crankshaft position sensor may be going bad. It is possible that when it heats up it fails and won't let the vehicle start. This can be checked by monitoring the CKP data with a scan tool when it will not start.
3) A faulty fuel pump. You would need to start with a fuel pressure test when the problem is happening. If there is not fuel pressure then the connector at the fuel pump would need to be checked for power and ground. If there is power and ground but no fuel pressure then the pump is bad.
If you haven't already done so it would be a good idea to check the computer for codes. Even if the check engine light is not on there still may be some codes stored in the system that would help narrow this down.