This could be a true dead spot where the resonance of the neck and body suppress certain frequencies, or possibly a set-up issue. I would first measure neck relief, and action height across all strings at the 12th fret, and the last fret. Is your string height slightly lower at the last fret compared to the 12th ? If so, there is a strong possibilty that the strings will not vibrate cleanly.
Despite fret leveling by Gibson (whether by hand or Plek), fretboard dimensions change with temperature, humidity and time. Naturally, this changes the alignment of the frets, and further work is often required. Frets can be checked by using a machined straight-edge placed across all the frets with the neck adjusted straight. If you use an engineer's square, you can check the frets from the 12th to the last, (there is no relief in this area, so you can check these frets without needing to adjust the truss rod). In order to do this, you must use sunlight to backlight the neck while you look carefully for uneven frets.
Of course, actions that are simply too low, or pickups adjusted very close to the strings cause problems. If your guitar has a true dead spot, I would try different gauge strings and make an adjustment to the truss rod. It's possible that a slight truss rod adjustment alone might be just enought to reduce the dead spot, since you are altering the resonant frequency of the neck.
Here's the recent similar post. http://forums.gibson.com/Default.aspx?g=posts&t=15669