1990 Acura Integra Trouble starting the car

I have been having a very strange problem for over the past 4-6 months. It all started with what seem to be a dead battery. Got it jumped turned on just fine. But the problem kept occurring, but only in interesting situations. The car would cold start just fine. After driving it for about 30 minutes for about a distance of 25 miles (my work commute) it would not start after driving it for anymore than 15-20 minutes should I turn the car off and try to turn it back on. After a few hours it would start just fine. If I was to drive the car for a short time and distance for example to the grocery store and come back withing 15 minutes I would be able to turn on the car, any longer, no dice. I finally took it to a mechanic and he said it was the alternator. Got it swapped with a rebuilt and I put in a new battery. The car was fine after that. Two weeks later I started to get the same symptoms as stated before. This time with one more funny thing. I could no longer turn on the car even with a jump on a cold start but in warm to hot weather. I finally got it to turn on with a push start and the engine was starting to sputter. Took it back to the same mechanic and he said it was a fuel relay. Got it running again just fine for a month and a half. Present day now and I'm getting the same symptoms back again. New issues though. On a cooler morning the car would not turn on and run on the first, or second time. It would start sputter and shut off. This has been occurring for the last five days. Tonight after resting for about 8 hours I had to jump it to get home. I don't what else could be wrong. All other electronics work. Once the car turns on it is fine. Additional notes. The mechanic told me that all electronics and charging systems are ok. Any ideas?