Perhaps the Eternal Flame was actually dying and it was frozen to preserve it's state until a cure had been found ?
The other possibility is that it was already dead in that ice (just like the Demon and Ul) and the moment the ice disappeared, it simply vanished.
From the looks of it, the Flame was there, since it is supposedly a guardian whose voice Natsu heard ?
The flame vanished! What now? No eternal flame that Natsu can eat :P
Awe I thought Gray was going to convert the ice into something useful with his ice make, like absorb it and make a huge armor version of himself to fight lol, guess not :(