One round does not* make a re-seat. It depends on way too much. Read your accounts of the USMC at Chosin, just by way of example.
I'll grant you Chosin. Ground frozen that thoroughly is essentially concrete. Unless the baseplate were set before such a hard freeze, the baseplate would never seat whether you were in an entrenchment or not (it would be like situating the mortar [or a MG tripod, for that matter] in the middle of a paved street). Same story for really stony ground. At the other extreme, you'll be tossing rounds all over the place if the baseplate is in sand, too (whether you've set up in an entrenchment or not). Sanbagging will help in all these situations, but you'll definitely lose accuracy.
I think that the issue here is what is meant by acquisition. The -1 or -2 to hit is pretty weak, to me. If I've got a mortar (or MG with T&E on a tripod) and I've got the range dialed in, almost every round is going to have effect. For example, out on the mortar range, you can sometimes get consecutive hits on an AFV hulk at 800-1500m, and almost all rounds are within the ECR (effective casualty radius) once you're dialed in. The ASL equivalent to this real-world accuracy would be something like once you make a to hit roll, all subsequent shots hit, unless you roll a 12 (and then that shot misses, but you immediately go back to guaranteed hits [unless you roll another box car]). By the Korean war, one had prox fuzes, I believe, which would even enhance the effectiveness more (as some of the success in hitting is that your blast is having effect, and the prox fuze really lessens the effectiveness of hastily dug skirmisher's trenches or hunkering down behind a little mound).
Anyway, with such a weak benefit for acquisition, I've just assumed (again, I'm a complete ASL novice and happy with the game, as is), that you've got eyes on a target and have some pretty good estimate of the range. Really, this is all that you need, with either a mortar or MG (both direct laying - you can [and I have] do indirect fire with tripod mounted MG). Once we had laser range finders for the .50cal in Desert Storm, I expected my guys to have first round effect on target almost every time - you see the target and you know what range to dial in on the sight, nothing much more to it when you have a stable platform (either a tripod with T&E [traversing and elevating mechanism] or a mortar that is direct laying with a seated baseplate, which in moderate conditions [both ground and temperature] means after dropping the first round and then getting bubbles up again on the sight).
Again, I am not taking exception with ASL - I'm a complete novice and am not so full of myself that I would presume to take exception with a game that's had more than 30 years of play by people who are much brighter than I. Also, the complete futility of "in the real world" arguments is beginning to dawn on me. Again, I only endeavored to continue posting on this, not to criticize any element of ASL or of those who play it, but in the hope that those who are interested in such things (presumably not an insignificant number of those who play ASL) might want to hear something of the mechanics of firing a mortar.
Look forward to seeing you again, Andy, and maybe continuing the discussion in person.
Ciao