Fuel Relay
I also think it could be your main fuel relay, as I had the same problem. The relay is prone to solder joint failure (a common problem). The fuel relay will normally give off a few audible clicks behind your head, as the bad connection(s) touch then break contact while driving. I removed the fuel relay from behind the driver's right ear on the rear wall of the cockpit, took the relay to a television repair shop, and the technician there heated all the solder connections to "resolder" them. I am sure someone will argue that this is not the "proper" way to do it, but I have not had the problem since. And as a bonus, the tech didn't charge me, and removal and installation were easy. Cost zero dollars.
For those who haven't had this happen, when the relay starts failing, sometimes the car will stall and refuse to restart, or not start the next day. If you remove the upper panel behind the seats, you can tap on the relay and get your car to restart. This will be good for 500 feet or 500 miles, until you replace or repair the relay. Mine failed two states away but the tapping method got me home without an expensive, time-consuming search by a mechanic unfamiliar with the car, at $90 per hour guessing while trying to figure it out.