I would start by checking the relay. However testing it may show nothing wrong. It may be a heat related problem with the relay. That may be worth simply buying a new one and swap it out. If that'* not the fix then you will need to start looking at the fuel pump. The FPR has no control over the fuel pump. It simply turns on and runs. The FPR bypasses fuel to the return line to hold a steady pressure in the rail.

I took the car out this morning, about a 15 min drive , parked maybe 2 hours, when I left the eng died and restarted, I got out of the car and pluged in my amp meter to the fuse socket on the raditor support, meter read about 6.8 amps running. I then pulled the vac hose from FPR, soon, maybe 10 seconds, the amps began to climb quickly, around 14.0 amp before eng died. 10 amp fuse was blown in amp meter.