Playing as Royalists.
I have just had a battle go to round 3 after a regroup phase at the end of round two.
Before I run the 3rd round it looks like all the morale factors of the units involved have been put back to what they were before the battle, all morale loses to hits have been wiped out. It also looks like elements that have been lost by the Patriot side have been moved around...... They did have two units that had lost one element each, one now has two losses and the other none....
I can't replicate the result though and you get no chance to reload a battle, you have to run the whole turn again.
It does look like the regroup is increasing both the morale of a unit and also a strength point that has been lost in the battle.