#1
I've been using the same Boss TU-2 tuner for I don't even know how long now and it's never gave me problems until now, albeit very minimal. I use pedal power for it so no battery issues but the problem is when I tune it won't register the high e string correctly.

I'm using a Fender Jaguar that I basically set up for my preference and the high e seems ok because it doesn't go out of tune often but when I do need to tune the tuner registers back and forth from D# to F so I have to keep tuning it by ear after the other strings are ok.

I know there's a lot of settings to mess around with in the tuner itself so I'm wondering if maybe I hit one of the buttons by accident to set something off? But only that string is affected.
#2
I have a few tuners that run into issues with my low e from time to time. Switch to the neck pickup and turn the tone knob all the way off. It helps me out.
Guitars:
Jackson Kelly KE3 - MIJ (Distortion/Jazz)
Jackson DKMGT Dinky (EMG 81/85)
ESP E-II Eclipse Custom (JB/'59)
ESP LTD EC-1001FR (EMG 81/60)
Fender MIM Strat

Amps:
Mesa/Boogie Dual Rectifier Roadster 212
Laney IronHeart IRT-Studio
Peavey Vypyr 30
Peavey ReValver Amp Sims
TOOOO many T.C. Electronic Pedals. . .