When you reduce an ancient stonebiter to about 1/4 of the original HP it goes in some sort of beserk mode.
It gets a increased damage, increased hit chance, increased armor, increased evades and a damage shield (not sure about this one).
It last about 15 to 20 seconds, after that it goes in some sort of fatigued state in which it is a wimp to kill.
So if you survive the beserk state (I suggest running around like mad) it should be an easy target.
Interesting--I wondered what was going on there. However, the first one I killed did nothing so spectacular--only the second one, which seems odd.