You might want to change out the relay for the fuel pump. It's meant to start the pump on battery power but switch over to alternator power once alternator current is established. That's to keep you from continuing to pump fuel when you crash into that tree that jumped in the way. If the relay has messed up contacts or hangs up in between, when it goes to make the switch over, it'll kill power to your fuel pump. I had an engine that was hard start/occasionally cut off that turned out to be the wires at the pump. They were all corroded from years of salt and would make and break depending on which way the truck bounced.

The other thing could be, as mentioned, a vacuum leak. Doesn't necessarily have to be one of the lines although I have had tubes drop off the bottom of the intake manifold for no reason. Could be a hole rubbed through the bottom of the air intake tube or a gap in the valve cover gasket. Did you check the idle air valve?