What you may be experiencing is a condition where the tuner doesn't accurately track the note being played.
The result is that one second you're sharp and the next second, without making any adjustments, the tuner shows that you're flat. So you go back and forth, back and forth, etc.
Some people mistake this kind of response from a tuner as the tuner being TOO accurate while just the opposite is true.
To me tuners of this quality are almost useless. I've seen behavior like this in some very popular tuners that aren't cheap.
On the other end of the spectrum, if you want a tuner that's VERY responsive and VERY accurate (1/1000 of a semitone) look at a Peterson. Unfortunately, they're relatively expensive. But the difference is very noticeable.