Thanks for all the awesome feedback, guys! The situation is really sporadic and it may go for a few days without a problem and then it is back. I actually have had to push it out of the garage once because it just wouldn't go into reverse. There is no grinding at all, it is just as if there is no reverse to get into, like the shifter will slide across to the reverse position, but just won't go down as if there was no down there! When it acts up, I can usually just keep playing with it (up to third, over to fifth, clutch in, clutch out, etc..) and it will suddenly slip into gear.
I changed the transmission fluid recently following the excellent advice on this forum and used a good synthetic blend. No brass or steel particles were in the drained fluid. I changed ALL drivetrain fluids at the time and have noticed that the drivetrain (transmission, transfer case, axles) seems much quieter and smoother now, but this sporadic reverse shifting fail is about as frequent now as it was before the fluids change.
Again, this beast has 227,000 miles on it and is all original, as far as I know, and I can't say that the reverse issue has gotten any worse over the past two years that I have owned the jeep since I bought it from my son. I am pretty sure he didn't take it off-road, but I know he "enjoyed" it thoroughly.
