I've now run into a bug twice that, now that it has happened to me, I recall existed in FE:LH before the 3.0 update and did not get fixed. In tactical combat the game occasionally, but rarely, gets stuck and the only way to progress is to click on the auto-resolve button.
The first time I saw it on 3.0 was in a battle on the small map with only 3 tiles across in the middle of some Fallen type territory with basalt columns on either side. The two sides had blocked up all the available tiles in the middle, and on the AI's turn a spider moved forward one tile to where all the tiles in front of it were blocked by other spiders and it could neither attack nor move any further forward. That AI turn then got stuck, no other AI units moved and control did not pass to any of my units. I had to click the auto-play to get out of the battle.
The second time was different, on a much larger and more open map. My Bard had the Rabisu's Horn, which grants the Maul ability. He attacked a group of militia and killed them on the second strike. The animation for their dying started, the human characters faded away, but there was still a little cloud on their tile so it looked like the animation never finished. Once again I had to click on auto-resolve to get out of the battle.
In both cases, for what it's worth, the auto-play button didn't work, it just made all the units jiggle around on their tiles like they were trying to take their turns but couldn't do anything.
I hope this helps. Since the bug happens in the middle of a tactical battle and rarely happens, I can't send you a saved game that exhibits the problem.