Electric issue?

I can't speak for anyone else but based on the info OP gave, I'm just guessing!
He says car starts, runs for a few minutes, shuts off . When he restarts, it runs fine all day.

That would seem to eliminate carburation/fuel delivery. I had a similar issue when I repainted the engine compartment of my car. ECU wasn't grounding because of paint . I cleaned off paint on firewall and ECU based on a suggestion I found on here. Never had the problem after. Easy fix so I thought I'd suggest it .