One user looking over their promotions shouldn't trigger any losses. If they select an earned promotion, that could... and a recalc could. But either way that would be something that would stay in synch wouldn't it? (unless it has something to do with once a promotion is taken the ensuing check then stays asynch and of course there's no message design in that since I would have assumed this part of the selection process was back in synch... hmm... That might be something to look into perhaps.)
But if that were the case, I'd think this sort of issue would come up more often... I could be wrong. However another possible issue could be, again, differing bug settings. There's a few bug options, opportunity fire, terrain damage, archery bombard, Storms to name a few, that could account for one unit having more or less strength on one or the other.
Events can also commonly be culprits. Could one of the events that either gives out promos or heals a unit in the field be to blame?
Yes any of the above is possible I suspect (except opportunity fire anyway - that does a sync roll to determine if it hits, and that would show up as one side performing an opportunity fire roll, and the other not, which is not in the logs)