Hi,
Not sure if this is the same issue described on the 6th string in a different post. I have a jtv-59 (2012) and until recently no issue.
Playing the guitar in variax mode through the hd500x and all of the sudden the high e string starts sounding like a "whammy" pedal is switched on. Moving the selector knob to an alt tuning and back fixes the problem. It doesn't I happen frequently, but when it does it is annoying.
I am pretty sure this started after the firmware update, and I have reflashed it once which has seemingly helped, but it has happened since. The only other change is that I swapped strings to the new m-steel strings and haven't switched them back to rule that out.
Had the guitar in case for about 6 months when my hd500 died, and only recently broke it back out to use with the 500x as I am trying to get back into using different models in my playing.