if your not going flat the your string inst slipping off the machine head pole or the gears arent slipping. to check to see weither the string is sitting in the bridge block grab the string near the bridge (as close as you can get to the saddles) and pull up on it and 'wiggle' it a bit.
when you tune make sure you always go up to the note not down. go as slow as you need to. dont rush tune by 1 cent if you have to. and relax. also you might only use your tuner for half of your strings. tune to the 4th string with the tuner then use the fith fret of the A and low E strings to tune them in by ear. (it will get easier to do as you get better)
if you do have a bad tuner you might take your ax to the shop and ask if you can use theirs, if it still does it then your tuner is fine and your already at the shop to get it fixed. if you have the money to throw away right now or even in the future, you might consider buying a second tuner. i lost my tuner once and bought a second then found the first and its great. keep one in your practice space and the other in your gigbag/case.
if its bad luck, i cant help im still trying to fix my own.
They say the END is near, but I'm Tired of waiting.