And CkPS, CPS, and their synchrony:

I believe that I have the same issue on my 1998 which is now at 260,xxx miles. Sometimes the idle is really smooth and then other times, it is obviously misfiring on 1 or 2 cylinders. But it is only at idle and MAYBE a hair above idle. Listening out the exhaust provides a rhythmic "pa pa pa pa pa pa" noise indicating the misfires. Sometimes they are enough to trigger misfire codes, sometimes not. Otherwise, I can drive it across the continent without issue. Gas mileage is what it should be, it makes plenty of power, etc. Oil consumption is negligible.

I still have to get off my lazy bum and hook up my oscilloscope to the cam and crank sensors to look for a problem. Also, since the misfires appear to be on cylinders #1 and #6 (coincidence that they are partners?) I am questioning the possibility of a damaged crankshaft reluctor. Spark plugs all look good and consistent, as does compression readings. I have not checked intake valves for buildup, either. It also appears as though the crankshaft sensor has been replaced at one time (before I got it) and the aftermarket units are notorious for making these things run improperly. If you search YouTube for South Main Auto (this guy is a GREAT mechanic) for when he fixed a 2000 XJ by swapping the crank sensor. It ran fine, but the check engine light would flash indicating misfires. The oscilloscope reading of the two sensor didn't show anything obviously out of the ordinary, but the installation of the sensor directly from Chrysler fixed it. In this case, it didn't run any differently, but the check engine light flashing stopped.


Another thing that I haven't seen anyone look at regarding this issue is the timing chain. Its not making any noise, but back in the day, loose chains caused rough running. In either case, a look at the cam and crankshaft waveforms should pick out an issue there.

I should also add that this thing has been doing this for over 10 years and 60,000 miles now but seems to have become worse in the last year or so.

Partners?

I suspect the cat if the exhaust smells of eggs. It is no longer doing its job. The only codes were for the misfires, but you can still have a flaky sensor somewhere. As long as the PCM can compensate, you may never see a CEL for it. Im with Dave51 on hooking it up to an oscilloscope. That will show you what the PCM is seeing, and hopefully help figure out what is going on. Also, what BlueRidgeMark posted is worth a looking into. Should you replace anything at any point, only use NTK o2 sensors, with the rest being Mopar, preferably. Aftermarket is questionable. Especially crank sensors. Expensive, but worth every penny.

Cylinders 1 and 6 are not partners. The firing order is 1-5-3-6-2-4..

Perhaps he is referring to the coil-on-plug ignitions (3 coils, waste spark).

There may be some terminology discrepancies. The way I learned it is that partner cylinders are at top dead center at the same time and conversely, bottom dead center.

In either case, #6 and #1 utilize the same reluctor hole in the flywheel.

can we get an update on what your learned? Same exact symptoms for my 2000 XJ

I suspect exhaust valve issues. I cannot explain with great confidence as to why it happens, but I suspect that as the valves rotate around, they find a spot where they seal the least and adding heat to the mix exacerbates it. So some cylinders probably run a bit leaner than others and just go over the threshold easier with valve issues.

It would explain why my 4.0 does the same thing, yet compression is what a person would expect and the misfires aren't consistent. It has been doing it for the last 60,000+ miles.

You may want to do a relative compression test, but that requires equipment to do it. Go ***** out with it, stop and notice how it is running poor, and immediately do the relative compression test.

I got done doing something similar with an old Ford Ranger with the Vulcan V6. I sent the heads in to get rebuilt and it runs mint now and the customer is happy. Sometimes you couldn't really tell there was anything wrong, and other times it would idle rough. It was worst after giving it the beans and running it hard as described here.
After all, all the keyboard warriors changed every single related part to no avail except for getting a valve job done. Throw more parts at it or do some testing or have the head rebuilt.