Main relay, common fault. Engine will start and conk out. Won't restart. Leave it for 5-10 minutes and it's starts no prob. Sometimes will start OK, then after a short drive to the shops or somewhere, then does the same.
Next time it does it, turn on the ignition without using the starter and listen for the sound of the fuel pump. If you can't hear it circulating fuel(whirring), it's the relay.