The FUEL RELAY can cause problems as you describe but the engine will also quit while you are driving down the road. Problem is caused by a crack in the solder of the circuit board of the relay. It can be fixed with a fresh dab of solder... or just remelted with a hot solder iron. Moisture and changes in temperature cause the cracks to either open or close (lose contact or make contact)
Relay is behind the battery. Its a black box about the size of a pack of cigarettes. Sits next to similar relay that controls air conditioning. Cap pulls off base and card is then exposed for inspection and repair.
Cracks are circular and around the pins that protrude through to and on the BACK of the circuit board. Always on the heaviest items mounted (soldered) to the board.
Cracks can be seen with magnifying glass. Usually only one crack but sometimes more.
