Engaging the 4 wheel drive has nothing to do with the locking mechanism in the rear axle. I believe what you are experiencing is driveline tension, where you have enough traction that neither the front tires nor the rear are slipping any, releasing tension. That isn't uncommon.
Mike - My apologies, I don't think I explained it well, but Hodge did a much better job.
Even though your front isn't jumpy like your truck, essentially it's a similar deal.
Your tractor has too much traction in 4wd on the gravel or grass. Fronts don't have the differential ability like the rears when you turn.
Your truck, like the last 6 of mine, will talk to you a little when turning if in 4wd when it shouldn't be. Your BX is doing the same thing. You can feel it on the steering wheel.
My BX2360 does NOT want to be in 4wd on dry grass or packed gravel if turning much. I think that what I'm on needs to be greasey to warrant 4wd. Same with my truck. Otherwise, tractor or truck wants to push, and not turn. Same-same.
Has nothing to do with the rear differential, its actually the fronts not wanting to play with each other while turning. It does feel similar, but if your diffy lock was engaged, she would complain much more about turning, and taking it out of 4wd wouldn't change it.
I hope this makes more sense. Certainly wish you the best!
For the other guys that responded to your question, if I missed it entirely, please correct me. Won't be the first time I missed the boat!