From what you say this sounds like a fuel pressure regulator issue: the pump stops because the fuel pressure has reached its target (36 psi), not because of anything the electrical relay does; if the pump never stops this means that the regulator is stuck in the open position and the pump has to work constantly to keep the pressure high.
Quantum makes an aftermarket fuel pressure regulator, but unfortunately it is set at a higher pressure than the OEM one, so you would need to adjust your fuel programmer to deliver less fuel.