87 F150 with 4.9 runs smooth but then cuts out.
 

I have a 87 F150 with the fuel injectioned 4.9 . It has both new fuel pumps ( rail and tank ) have removed the back tank and selection switch. All new tune up parts , everything , I can think of and my mechanic can think of has been replaced . The truck will run for a few miles and then lose power and start bucking like its flooding pressure ( but its been checkes and is good ) , or like to much back pressure. Could my exhaust cause this , doesn't smoke at all. Just lost for answers.

Did he replace the defective ign coil?

yes kit has a new coil , the only thing not replaced is the exhaust system . I was just thinking may be a clogged cat.

A restricted exhaust would give problems as soon as you start it, not after a few miles. I would connect a fuel pressure gauge, situate it so you can see the gauge while you drive and see what the pressure does when it actually acts up. Your 87 4.9 should have 45-60 PSI of pressure.
Next, check for spark when the engine will not startwith a spark tester or an old spark plug with a helper..The pick up coil in the distributor or the distributor mounted TFI module would raise suspicions. You could try a heat gun while idling in the driveway. Direct SOME heat on the TFI module and then the distributor and see if the engine acts up.
For your curiosity, you can use a vacuum gauge to check for an exhaust restriction.

It would be useful for you to state what was done so far.