Sometimes, if the string is cut too short it can't be wrapped around the tuner enough times so it slips slightly after playing. Especially, if you bend strings or use the whammy alot.
Also, new strings tend to stretch and go out of tune easily at first until the strings break in.
Sometimes I'll tune my strings almost a half step high and bend all of them several times to stretch them out quicker when they're new.
Then I'll retune it to standard pitch and bend them all again then retune.
If that still doesn't help you could put a new string on and make sure it wraps enough times around the post so it doesn't slip. I make sure that as the string wraps around the post, it crosses above and below where the string first passes through the tuner hole.
It helps clamp the string in place.