This sounds like an electrical actuator or sensor at fault .Usually when you can cycle the ignition key on / off and then restart the engine and the fault is gone temporarily this indicates that this is an electrical component causing this issue.
This could be a wiring issue as things tend to expand when hot and its possible a poor or partial electrical connection is being pushed apart on one of the major sensors so check the connection plug and wiring to the following;
Crank position sensor
Cam position sensor
Throttle pedal position sensor
unplug each in turn and use some switch / contact cleaner spray on the pins to ensure its all grease / dirt free
Also worth checking the connections to the fuel pump for the same reason - unplug each in turn and give them a good squirt of switch / contact cleaner - Not WD40
and also unplug and inspect the main power relays and fuses for signs of overheating or corroded terminals - so the ones for the ECU and the fuel pump
And also unplug the wiring loom connections in the engine bay one at time and inspect for corroded or recessed pins.
thanks for the clarification
in that case I'd start by checking the condition of the main battery connections and the earth connections between the chassis and the engine and the chassis and the battery
also check the condition of the high power ( 40A) fuses in the engine bay fusebox for cracks and corrosion