I have zero experience with this gearbox in Jeeps. However, I've run a couple of Peugeots with them in the past.
They're really not a bad tranny, but need to be shifted sympathetically or the synchros can wear out fairly rapidly. As was pointed out, they do take a while to warm up (usually about 5 minutes or so); this isn't necessarily a sign of a failing gearbox, though. Second gear being balky sounds about right from what I remember.
If it's in good shape and driven properly, it should last pretty much indefinitely. They like oil changes every 30,000 miles (and I really recommend using the factory-specified oil; can't remember the weight off the top of my head). Adding
Lucas oil stabiliser in the recommended proportions doesn't hurt, and helps with cold running. They also make various gear oils, but I've never run those as going the additive route seemed safer so can't comment on them.
God forbid your tranny ever breaks; it *will* be expensive to fix or replace (unless you find a junker Peugeot 505 with the BA10/5 in it) compared to the others that AMC/Chrysler used over the years. Most people still running Peugeots tend to go the replacement rather than repair route, since buying a dead car with a good tranny is much cheaper than rebuilding it.
My opinion is that it's basically a good gearbox, but the Jeeps that it was used in were not a suitable application for it. I suspect that Renault had a hand in specifying this box during development, though I can't for the life of me imagine why - it was never designed for heavy-duty use, and had to be bought in from a rival manufacturer. Then again, I gave up trying to figure out Renault's thinking years ago.