About half of the balrogs were wiped out in the War to Begin All Wars (aka the War of the Powers) at the end of Season 1, leaving Melkor with about 9 (Arien had previously defected, and there were roughly 20 to start with). The Valar can kill balrogs.
Our 'balrog rule' is that when the balrogs appear in battle, a named elf (main character) must die. In the Battle of Sudden Flame, we will have balrogs fighting, and Aegnor and Angrod will die. So...Aegnor is definitely going to be killed by a balrog in this story. Probably Angrod too, but I suppose that is up for debate when we get to that point in Season 5.
It has been suggested that maybe Aegnor takes out the balrog he's fighting, and dies with him. We have enough balrogs, so we can afford to do that. We'd make use of a convenient cliff somewhere if we went that route.
It has also been suggested that Gondolin develops some unique 'anti-balrog' technology, thus becoming the culmination of the Sauron/Gothmog feud when they eliminate him. Gondolin swords are definitely magical in other ways, and it is rather significant that the Fall of Gondolin, War of Wrath, and Gandalf's confrontation with Durin's Bane are the only balrog deaths we are told about. I don't think all of the balrog deaths in the War of Wrath will be from swords from Gondolin, though, so we probably don't *need* a Gondolin-only rule.
More elves will be killed by balrogs and fail to kill the balrog in return - Angrod and Fingon come to mind, and we've already had Fëanor.
So, to re-cap: Aegnor will fight a balrog, and the balrog will kill him. Whether or not he kills the balrog too is a Season 5 finale question. That has been suggested, but I wouldn't call the decision final at this point.
Balrog recap:
9 left after War of the Powers
1 killed by Aegnor?
Gothmog killed in Gondolin
1 more killed in Gondolin
4-5 killed in War of Wrath
2 escape War of Wrath
Durin's Bane killed in Moria
1 indefinitely MIA