In a recent battle, I had my fleet divided into 3 flotillas, and as it turned out, the enemy (AI) did the same.  Watching the battle, I noticed that my middle flotilla #2 wiped out their middle flotilla #2, then proceeded to destroy their flotilla #1, but then, despite having the enemy vastly outgunned, sat there without firing a single shot at the enemy flotilla #3 while the enemy ships proceeded to turn them into Swiss cheese.  What gives?  Is that a bug, or is there some interaction I'm not aware of that prevents certain flotillas from targeting other flotillas at all?  Mine were armed with Sync lasers, if it matters.

An uploaded save game would be useful.

I took a save game last night, but when I loaded it this morning and re-fought the battle I won this time.  Never been upset to win before! ;)

I will keep an eye out and if it happens again I'll capture another save and try to reproduce.

I think this has to do with the range of the weapons on your Flotillas and the distance between you and your enemies. I haven't tested things out myself to be 100% sure but I have noticed that flotilla 1 usually does not help with flotilla 3 and vice-versa. Flotilla 2 usually ends up firing at 1 or 3 if it has managed to clean up its match. Regarding weapons, I generally use only the energy ones with the occasional missiles (kinetics are good only as flak) and can confirm that this happens for flotilla 2

A save would be useful for the devs. But this is a known issue.

From what i could see from looking at the combat overview, flotillas can get behind one another. Weapons have limited weapon firing arcs and no guns to cover their rear. So when ships don't fire back it is because they have no weapons that can shoot backward. Now, this happen because of the way fotillas paths are set in battle, short range fleets tend to get flanked by long range ones.