could try wiring the fuel pump up permanently.

Sounds as though the fuel pump is working when you crank the engine then cutting out when you release the key.

Get a wire in the live at the pump end,unplug the live wire,shove the wire in and plug the plug back in.

Wire up to a live,either battery or the rear light, depending on the lengh of wire,must turn on the lights though to have a live.