I don't believe that the injectors are the problem. To drop pressure that fast would cause the engine to turn over slower because of to much fuel in the cylinder, and after starting there would be a noticable black smoke out the tailpipe. Looks like if you have no noticeable external fuel leaks, then your are looking at a fuel pump module.

 

Okay, after chasing this problem and throwing money around I replaced the fuel pump module and the car starts as it should. No missing or repeated cycling of the starter.
The jeep dealer wanted $435. for the unit, but I picked it up from my local independent auto parts for $180. Advance said they couldn't get it through they're warehouse.
It's a Carter unit, I know they make carburators, so it should last awhile.
End of story.

 

I fixed mine with 30 bones plus shipping. Installed S.U.R. Check Valve on the line coming out of the tank, did it all from underneath without having to drop the tank. Starts up every time now. It's a shame to replace an expensive fuel pump simply because the check valve is worn out.

 

really. I hav the same issue.. I hav a 97 xj .. I heard u shudnt do an external check valv ... can u get alitt mor specific wit ur year xj and wat u exactly did. I hate havin to double key evrytime.

 

Check your fuel pressure regulator, it's on the rail at the front of all of the injectors. Sometimes this has a habit of causing problems.