Why won't FaceTime work with one specific contact?

I cannot find an answer to this problem.

My girlfriend has an iPhone 4S. She is able to FaceTime anyone she wants, except me.

I have the new iPad and an iPhone 5. I am able to FaceTime anyone I want, except her.

We have tried virtually everything. It will not connect whatsoever from either of my devices or from hers. When we dial, it just rings on the dialer's end but not the other. It doesn't show a missed call because from the one being called's end, it never shows as even being attempted.

This was an issue when I had sprint. But now we both have Verizon. However, it still just doesn't work whatsoever. I am able to FaceTime via my iPad with anyone else. This is very frustrating and the only suggestions I'm getting are to make sure FaceTime is on in the settings, time and date are correct, etc etc.

These are good suggestions, but I can quite literally FaceTime with my parents for a half hour, and then immediately try my girlfriend and still have no luck.

Please someone help!

Thank you to my future hero