I would guess that Trotha may have seen the additional hussars coming up, and is smart enough to guess that significant reinforcements of infantry, if not an entire army (as there actually is) may be coming up the way and is close. If he doesn't have a good idea of exactly how close that infantry is, he may well conclude that he's already missed his chance to hit us before reinforcements can come up mid-battle and really ruin his day. Just about the worst possible thing you can do is be mid-battle when significant enemy forces show up able to be committed against you while you're still locked in combat and unable to maneuver.
Frankly, he might be a couple days off in his estimate, but if he hadn't been able to carry the field in one day of battle, which could be unlikely given the terrain and our intention to sit there dug in, he would be caught. And if he's savaged, of the four/five armies Norn and satellite states have committed, three here and one or two further south, all three in this theater would have been destroyed. The Grand Duchy's already been hurt badly enough they are likely negotiate separately an end to the war on favorable terms to Arne no matter what Norn does now, if not capitulate entirely given an army is still driving on their capitol and has taken their second city.
Trotha's going to not only have to guard against us, but also possibly Montilivet finishing her campaign to defeat the Grand Duchy and then putting in a second expedition from the east... behind the second river line guarding into the heart of Norn, using plunder from the Grand Duchy to fund and feed her force.
[X] Let him withdraw
Let Durand go fight the other theater and defeat them likewise.