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 position sensor
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.
Also its worth checking that the electric pump that feeds the injectors is working correctly, it should run for a few seconds then switch off when you first turn the ignition on. If the connections to this are corroded or damaged then the pump could stop at any time. Check that its relay switches in and out and the relay contacts are clean and bright – replace the relay if in any doubt and do the same for the fuse, ideally measure the voltage at the pump and check its getting 12V