1995 Buick Park Avenue Engine stalls

Hello, I have a 1995 Buick Park Avenue that intermittently stalls while driving. It loses power for a few seconds and then shuts off. It will not start back up immediately, however it does crank. It usually starts back up after 5-10 minutes, and may run fine for another hour, or even for a few days to a week. My initial thoughts were that it was a fuel delivery problem, but here is where it gets interesting. When this happens, and only when this happens, the following electrical components do not work, even with the key in the on position:

Power driver side mirror adjustment
Power Windows
Power Door locks
Power Seat

The above components attempt to work, sometimes making a faint buzzing noise when pressing the button. The power locks move slightly when the button is pressed, but it acts like it does not have enough voltage to lock the doors.

The following items operate correctly during the time that the car will not start back up:

Dome light
Head lights
Flashers
Radio, Power antenna
Heat/AC

So, what I have been doing lately after the engine stalls and it will not start back up is to simply press the power window button every 30 seconds or so. When the window comes down, then I know the car will start up, and it does.

I've talked with a few mechanics who tell me that if I bring the car to them and it is running, they can not really troubleshoot it effectively. I understand that. Again, it may be one week between episodes. Could be 1 hour. It is definietly not consistent.

Please keep in mind that all electrical components work perfectly when the engine is running.

Any ideas of what would be the most likely cause?

Thanks in advance,
Tim