1992 Escort problem

Hi,
My girlfriend's '92 Escort (engine is a '91 1.9L with about 150k) exhibits some strange behavior after driving for about 15 minutes or more.
It idles and accelerates fine for a while and then there is an almost complete power loss, but the car never actually stalls. It just gets worse and worse until you can barely keep it going 5 mph. It kind of chugs and jerks and will sometimes backfire if you give it a lot of gas. It will continue to do this indefinitely, but if you shut the car off just for a second, it will start right back up and run perfectly for another 15 minutes or so and then do it again. We replaced the fuel pump a while ago and measured good fuel pressure and the car is not throwing any codes. I'm just guessing that the problem is something electronic since shutting the car off sort of "resets" the problem for a short time.
Any ideas on where I should start?
Thanks, Jeremy
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No codes thrown in KOEO or KOER mode? Not even a lean code? Nothing?
Maybe something is triggering your car's computer to go into "limp home" mode.
Also worth checking that the EGR system and the IAC valve are functioning correctly.
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What was the fuel pressure? Have you tested fuel pressure when the problem happens? Install the fuel pressure gauge tape it to the windshield and drive the car. Watch the pressure while the car is loosing power, I'll bet it drops.

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