'89 300E Accelerator stops responding intermittently...

After 253K the old car is telling you " I don't want to go over 60 MPH!"

Actually, fuel use increases with acceleration , hill climbing and speed so a fuel system restriction will become evident as speed increases. That could be a fuel filter, kinked fuel hose, or weak fuel pump. I'd first change the fuel filter and see if that doesn't solve the problem.

I'll give it a shot, but the filter only has 5000 miles on it. Funny thing is, Power is great at all speed ranges, the fuel just seems to shut off every now and then (about once every 2 or 3 days) for about 30 seconds. I was wondering if it could be the Fuel Pump relay?

Sure could be the fuel pump relay.... but relays usually don't recover by themselves. The engine dies and needs to be restarted.

Any exhaust leaks? Exhaust that might leak onto a fuel line and cause a vapor lock?

If you find nothing, suggest you have the fuel pump's output pressure and volume tested.

You guys are talking about the injection pump, right?

Ah aint nevuh seen no fool pump on a 300SD. Mebbe somebody stole mine.

This ain't no oil pumper. Just a good ol petrol.