Can a fuel pump be failing if it still makes noise?

My main fuel pump ('91 745T, Bosch LH 2.4 system w/2 pumps) makes noise, but it is not consistent. Most of the time it is a rapid whirring, but sometimes it makes a clunking or rumbling sound. I'm talking about the short period the pump runs when the key is turned to KPII before starting the engine. Can it be failing?

The in-tank lift pump was whirring too, when I checked it this morning. Can they make noise and still be failing?

Can either one of the pumps run when quite cool, and keep running if they start up, but then when shut off, not run right until they cool down (or something) again?

My car seems to start up when cold, but won't start again until it cools all the way off.

For some reason I think it is the fuel pumps or fuel delivery system.

Edit: Note that sometimes when trying to start it, turning the key to KP II, it seems like the pump does NOT come on. I said "seems like" because I may be trying to restart it too quickly, like not waiting for the ECU to reset or something. But nonetheless, I have noticed both the widely varying noises from the fuel pump, and the rare but noticible times when the pump does not come on at KP II. Do you guys think that maybe all the symptoms point to a pump failure?
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Scott Cook - 1991 745T, 1985 RX-7 GSL-SE, 1986 Toyota Tercel (Don't laugh, it is reliable, faithful AND gets 41 mpg!)