Guess I'd start by checking the current consumption of the pumps. If they're drawing too many amps it possibly could overheat/burn out the relay. That'd be my first guess anyways. Everything else that I can think of (except maybe a ground) would be an input, and I would think that an input could do this.
Oops, another possible output of that relay is I believe it also controls the heating of the O2 sensor (I believe yours has the heated O2 sensor anyways) so maybe they want to check the current consumption of that as well. Unsure if a O2 sensor drawing too many amps would affect the relay in this manner (stalling problem due to fuel delivery problem) or not.