1992 s10 stalls and won't restart

I have a 1992 s10 1500 series and about 2 weeks ago while at the bank drive-thru, it stalled on me. The idle sounded normal up until it stalled, and it restarted with no problems. About 3 days later the same thing happened while at a red light, but this time it took longer to start up. The same night I stopped at a store and when I came out to start up my truck it just kept turning over.
Now the funny thing is that whenever it sits for over an hour, it will start with no problems but will only run for about 5-7 minutes and then stall again. I've checked the fuel filter, and also the little bag-style filter on the bottom of the fuel pump. The pump turns on when I turn the key to the on position, but it just keeps turning over unless it has sat there for a prolonged time. I'm not much of a mechanic, so any advice would be greatly appreciated.

Thanks in advance,
Kevin

What engine do you have?
When it quits you need to check for lose of spark to spark plugs and lose fuel pressure?