The 1st string (high E, thinnest) on my Schecter (Damien FR) whenever I put it in tune it doesn't chime like all the other ones do but it makes sort of a deadened noise and no matter what I do it still does the same thing. I've popped 3 strings trying to fix it already.
have you checked to make sure it's not touching anything it's not supposed to? frets, etc.? is it seated correctly both in the bridge and the nut? these might seem like dumb questions (or they might not) but you need to narrow down the causes somehow.
i had the the same thing happen to my les paul so i had the nut changed and it was fine after that
current gear
music man steve morse y2d
fender american strat
yamaha dg 100
crate palomoino v32 head
I thought it was because of the frets too but when its like 3 cm off of the fretboard it still does it. If it helps the nut did strip but on the other side and that side is fine.