Intermittent stalling became stalling every time it cranks

I apologize in advance for the length of this question but this has been a problem for months now and I and the local mechanics are at a loss...

I have the car listed above 10th Anniversary Edition that had approx 120,000 miles I purchased it. It started up quickly and ran perfectly for the first two months or so. One day when I was driving for about 45 minutes and it was extremely hot that day, the car randomly stalls at a stop sign, I cranked it up and it started right back up, but then immediately shut off again. When I went to start it that time, it would not start at all. I had it towed to a repair shop, and the next morning the car started right up for the repair people. They were not able to determine that anything had ever been wrong, so they told me to bring it back when it did it again. I never had the problem again for about a week, but then when I attempted to drive it again for about an hour and a half this time, it stalled again at a stoplight, also very hot outside. This time, it wouldn’t crank at all, but then started right up about an hour later. I drove about 10 minutes, turned it off to get gas, tried to crank, it wouldn’t. After about 15 minutes, it started right up, and I drove it back home about 45 more minutes, with no issue, but both times, it had cooled down significantly when it started back up. No more problems for a month, until one day it was extremely hot again, and the car stalled after about 15 minutes of driving. Started back up about 2 hrs later once it had cooled down some. Drove back home with no issue, but then later that evening it wouldn’t start, started up 15 minutes later, wouldn’t start again, started back up, wouldn’t start again so I left it. Next morning started back up and NO More issues for about 6 weeks, even driving around for 5-6 hours at a time (hour straight, stop and go, another hour straight back home) One night, after making one of those drives with no issue, car started back up, but cut off after idling for about 15 minutes. Wouldn’t start back up right away. Once it started about 15 minutes later, it did the same thing. Next morning, started right up, idled fine in the driveway for about 15 minutes. Later that day I made several short trips with no issue. About 20 minutes after parking the car, it started right up, but wouldn’t stay idling more than 5 minutes. When I try to start it right back up, it won’t, but try it about 10 mins later, and it will start, but still won’t stay running at an idle for more than 5 minutes, sometimes 1 or 2... A couple of times when it was about to shut off I gave it some gas and it sputtered a bit, but then stayed running a little longer, but only for about another minute or two... Let it sit overnight, started right up, but keeps following the same pattern. The dash lights do come on when it stalls. When the problem was only happening intermittently, one mechanic suggested a sensor that sends a signal to the fuel pump might be getting jammed when it gets hot and his “test” was to bang on the area in front of the sensor and try to “unjam” it and it should start right up, but that didn’t work, and that was before it started the current problem of not staying started while idling. Any suggestions you ma have would be greatly appreciated because I’ve talked to several mechanics, and no one is really sure what the problem is... I just need my car fixed! Please help if possible!