" Then it started a few hours later. This happened several times on and off till I decided to have it checked out."

Classic Fuel Pump relay or fuse issue

" He offered to replace the fuel pump at no charge "

Which pump? The primary rarely fails before 300K miles and the in-tank lift pump would only effect your car if you are below 1/3 tank.

"after a lot of searching he said discovered that there was a problem with the computer sending a constant electronic signal to the fuel pump relay which burned it out."

I hope you misunderstood this because otherwise you mechanic is an idiot.

Check your fuses. Since this is a 1992 I cannot remember if you have the under-hood 20 amp fuse but I believe not. In which case you have a significantly overburdened #6 fuse. Art B has an excellent solution for this but he also has a test procedure near the top of this page:

http://cleanflametrap.com/transferPump.htm

You cannot verify the condition of a fuse and its holder without removing and inspecting the fuse, cleaning the clips and re-installing it or replacing the fuse.

If it is not a fuse issue, the likely culprits in order of likelyhood are:

Crank position sensor
Ignition amplifier/module/whatever they are calling it now
Fuel pump relay despite the fact that he replaced it...or claimed to

"But there was no problem with spark, fuel, the relays, etc...everything checked out. "

This is the nature of intermittent problems.