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2003 4dr 5spd w/ 1.7, 174,000 miles, sometimes when I accelerating I lose power, but when I turn the car off and restart, it accelerating just fine. What could be the problem or things that I should start checking.

 
Rep Power: 119

My first thoughts are you have a failing fuel pressure regulator.

Maybe rent a fuel pressure gauge, connect it, and leave it connected.

Should read somewhere around 40-45psi? normally, drive until your getting poor acceleration symptom, pull over, open the hood and see where the gauge is at right then.

Second though is you have a chunk of your catalytic converter that broke loose and is intermittently blocking the exit.

Pretty much anything else would cause a engine code and light up your MIL.

 
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I will start looking into to this weekend, Thx.

 
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Is the fuel pressure regulator and part of the fuel pump assembly in the tank?
Due to the age and mileage I was planning to replace the fuel pump assembly.

 
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I found it near fuel rail

 
Rep Power: 119

The actual regulator is attached to the fuel pump inside the gas tank.

That part on the fuel rail is some sort of mysterious device.

 
Rep Power: 224

I believe the thing on the fuel rail is a fuel pulsation damper. At least that's what I've found in other service manuals.

 
Rep Power: 119

That sounds right, still mysterious, and defiantly not the issue here.

Wonder what the actual symptoms of one those failing, besides gas dripping out.