Test if it's resonance based: firmly plant the headstock against a door jam or dresser etc. Does the note now ring out? If yes, then it's resonance based (damping the neck lets the energy stay in the string and allows the note to ring out). Also if it's resonance based, bending to the problem note will also die quickly.
Theres really nothing you can do to remove a resonance based deadspot. Adding or subtracting weight on the headstock can move it up or down a few steps depending on placement etc. But nothing can eliminate it entirely. Best you can do is a Fat Finger or clip on tuner that you move around depending on which note you need to ring out.