I think it will happen when they have a lot of man powers but no fuel. If they have much fuel, they'll combine it with Pershing, even sometimes Pershing is everywhere on the map, very rare infantry.One area though of concern is that the American AI will spam almost exclusively Calliopes and Rangers, dozens of them.
German AI seems don't know how to kill Pershing, and most troubled if the allied is armor division because there is crew repair. Pershing is unbeatable, even there's Tiger, Panther etc (I still see Tiger's shot range is shorter than Pershing, same goes to PE Tiger Ace which cost 1000). Only King Tiger makes them flee. Even if they fleed away, crew repair is there, and they have a good health again.
Several occasion when I'm encountering more than 8 Pershings, German AI is really, really on defense until losing HQ. So I have to chase them myself. One important thing is both have quite same amount of fuel.
Anyway, I see an Elite King Tiger always repair itself, however little the damage is. So it rarely shoot when surrounded.