| What kind of guitar is it? Fender-style instruments have a small fretboard radius - there's a lot of curvature from the bass to treble side, that is. Because of this, the middle strings have to be set slightly higher than the bass and treble sides. Take a look at the strings from the bridge facing toward the nut. If the levels of the strings are level all the way across, you're going to want to raise the A and B slightly, and the D and G slightly more.
If you have a flatter fretboard, you're going to want to raise the action slightly regardless, in a radiused pattern if you only have problems with the middle strings. A little bit goes a long way, and setup is all about fine-tuning, so have some patience when doing adjustments and you'll find you have to do a lot less than you think you do.
Additionally, since the problem only occurs above the 12th, you might want to check your relief. Take a look at the setup thread at the top of this forum to find out how. | 
