No, Eevee being shiny doesn't affect her ability to evolve.
In X and Y Eevee evolves into Umbreon between 8pm and 3:59 am, if she isn't evolving then her happiness probably isn't actually maxed out. Check what the lady in the Pokemon Fanclub at Laverre City says to determine her happiness. If Eevee is indeed at max happiness then she will say "It's amazingly friendly toward you! It must be so happy spending everyday with you!"
So if she still isn't evolving and you're 100% positive that her happiness is maxed, then my advice to you would be to check the time of your DS clock, because it may be wrong.
I did some research and learned that some, but not all people, encountered a glitch where at some point they deposited a Pokemon that evolves via happiness into Pokemon Bank, and upon withdrawing it and maxing out it's friendship, it still wouldn't evolve. If you deposited your Eevee in the bank at any time then I'm guessing this is what's happening to you. If this is the case, then based off of what I read, trading Eevee to a different game and trading her back and re-maximizing her happiness should negate the glitch.
Other than that, if you got your Eevee through trade then it is probably hacked.
I hope you figure it out, having a shiny Eevee and not being able to evolve her must be frustrating. Good luck!