Maybe not entirely the same issue... but I have had problems in the past with tuning the guitar, playing it once and it being slightly out.

I resolved it by making sure I had enough windings on the peg, not over stretching the new strings (which left me with overly stretched sections of string believe it or not) and Big Bends Nut Sauce) to lubricate the nut.

Made a massive difference!

I use a Snark clip-on and have no problems now.