A: It is possible that the battery in the guitar is going out. But more than likely, you are hearing the strings of the guitar acoustically along with the tuned signal coming through your amp. When the sound from the out-of-tune strings combines with the in-tune guitar signal, you get cancellations that produce a chorusing effect.
The solution — and we’re not kidding here — is to turn it up! The signal from the guitar needs to be loud enough so that you cannot hear the out-of-tune strings acoustically.
Another solution is to play the guitar through headphones, which will block out the acoustic sound from the strings.