I’m with Clay Bee on this one. It sounds like you have a power/ground distribution problem.
Check battery, relay and ground connections. Make sure everything is clean, tight and corrosion free. Use good lighting and look for chaffed insulation. Check for poor connections behind the fuse block. Try wiggling wires and connections with the engine running. If the vehicle shuts down you have located the problem circuit. Be careful when doing this because a running engine can bite. The ignition switch or its connector is another possibility.