1998 Pontiac Bonneville Very challenging question. Car wo

I have a 1998 Pontiac Bonneville that keeps shutting off and refusing to start. We initially thought it was the fuel pump, since normally you can hear the fuel pump pressure up when the key is turned on, but when it won't start, you don't hear the pump at all. Had it towed to our mechanic, but when he went to check it, it started and ran fine. He replaced the fuel filter "just in case" but said he can't fix what's not broken and to let him know if the problem recurred. It did, about 10 miles from his shop. At this time, we noticed that the power windows wouldn't work either (window was down). We played with the key, turning it on and off while holding the power window button, and every once in a while, the window would go up a fraction of an inch. Finally, the window went all the way up, and the car started when we tried, but ran very rough, stalled, and again wouldn't restart.

Had it towed again, and again, it ran fine for him. Again it ran fine for him, but not when we went to pick it up. He finally said it was the ignition switch, and replaced that. We picked it up, and it ran fine that day. We haven't driven it much in the past month, but again this week the same problem happened. It will turn off randomly, and sometimes will restart, and sometimes it won't (and again the windows don't work when it won't start). This is driving us (and our "old school" mechanic" nuts. Any ideas?

Added note: It will turn off regardless of whether the car is idling or running down the road at 70mph, although it seems to be more frequently when the car is idling or going relatively slow.