There is no way to prove that the battle is stuck in a loop. We don't know how the AI works. Just imagine that it has a principle built in, such as "after N turns in a cycle, switch tactics," or something else... For example, instead of attacking the nearest unit, it attacks a ballista...

In other words, if you haven't encountered this behavior through experimentation, it doesn't prove that it can't happen in principle... Therefore, it won't work... Please, simulate the entire battle from start to finish, but don't jump from the start to the end just because "I'm sure..."

I tried to eliminate the Earth Elementals manually using other methods, with harpies and snipers.

The snipers had a limited number of shots, so they couldn't eliminate most of the elementals.

However, the harpies, with their retaliatory attacks, dealt much more damage than the ballista.
The battle lasted 3 hours manually, and at some points, it started to seem like, if my hand faltered, it would all be over...

In this battle, as in the case with the ballista, the snipers were a distraction, and the harpies acted as the ballista.

BUT! after about 50 Earth Elementals remained, they suddenly stopped chasing the snipers and rushed towards the harpies. And that's where,
if we had an automated system, we would have failed.

So, there is some truth to what AmberSoler said.