1997 Subaru Impreza

Can be an issue with the relay or pump. You obviously have an ignition/fueling issue. Begin by checking tune up items. If you have access to a scan tool the fuel trims may allow you to develop an idea of the condition occuring fuel or ignition related. Also check for any history codes.

How often does this occur? You can put a fuel pressure gauge on while driving to monitor pump operation.

But before going any further with wild possibilties to the issue why do you think it is fuel related and when does the condition occur? Does it happen all the time?