Should be an RH.
What do you mean pop out of gear? It's not a manual trans, the shift linkage doesn't come into play while shifting unless you're manually running through the gears. It just moves a valve to the appropriate location, and shifting is accomplished by fluid pressure compressing or releasing clutch packs.
If you have access to a good scan tool, you may be able to look at CVI numbers in the TCM. Being an RH, I'm not sure what you can see though. I've never tried scanning one. If it's an RH, you should be able to see the CVI numbers (clutch volume index) which are a fairly close measurement of the clutch pack tolerances. If you see one way outside the spec, you know that clutch pack is wasted.
If it is slipping at all, you're probably going to need one or more clutch packs. And possibly a seal here or there.
I rebuilt my trans, but I didn't figure out what caused my problem. Possibly it was the check valve in the cooler line.