Some good info here, not all 100% correct.
On the Renix, it isn't going to fire until the CKP (aka CPS) has sensed and sent to the ECU the information that the engine is cranking at 300+ RPM.
For what reason, I don't know, but that is how it was meant to be. You could, if money is of less concern than the time, install a high performance starter and a monster CCA battery to spin the engine to 300+ RPM faster. I'm not sure if anyone make a gear-reduction starter, like Mean Green, but should be easy to search.
Fuel pressure dissipitating? Sure. You can check if that is your problem on some (maybe all?) XJs by turning the key to the RUN position and allowing the system to prime for 3 seconds. Do this maybe two, three times and the fuel system should be fully primed and if that was your problem you should see an improvement. If that is your problem then somewhere (search is your friend) there is one or more threads on the "BMW Mod" which is simply using a BMW fuel check valve in addition to whatever is in the pump. You can also go to Jegs or Summit and order an external fuel check valve.
You could also just need a tuneup.
Or, it is just the nature of the beast.