[Boromir88]

(I'm so silly, I originally placed this in the assassination thread down the hall...this I believe is the proper place).

But still who's to say the Balrog would have wanted to fight for Sauron had Sauron wanted it? Sauron couldn't force the Balrog into obediance. The Balrog was a Maia, just like Sauron, maybe one not as powerful, but Melkor wasn't entirely in control of the Balrogs, as he was over his Orcs.

Durin's Bane fled, and decided to make Moria his personal retirement home, he spent his days in relaxation and comfort, arguably what his intentions were after he fled from Morgoth's service. He was stirred awake by the Dwarves, and it was also made clear he was the Orcs' commander...he seemed quite content to stay under a mountain ruling over a host of Goblins, not wanting to enter into the service of someone similar to the one he left ages ago.

And as Pitchwife wrote, their rank in Morgoth's administration is hazy. Sauron seemed to always be Morgoth's chief guy (adminstratively and maybe his general 2nd-in-command), as Sauron was Morgoth's greatest servant. However, the Balrogs were right behind him, as wasn't Gothmog, 'Lord of the Balrogs', in command of Morgoth's armies? Also, in FOTR, either Celeborn or Galadriel make clear that you will not come across a more powerful and terrifying foe unless you were to go see Sauron.

Edit: Remember, the Balrogs were not forced or bred into Morgoth's service. They were independent Maia who willingly allied themselves with Morgoth (maybe even for their own personal gains as Sauron arguably did), and they willingly left his service when they wanted to.