First thing to do is make sure the intonation is spot on. Don't use harmonics on the 12th fret, play the open string and then play the 12th fret. Another thing to do is make sure that when you fret the 12th fret for intonation purposes, that you use the normal pressure you use in playing. The reason for this is that you could use a light touch to set the intonation, and use a heavy touch while playing. The pressure you apply on each individual string pressed against the fret in normal playing can raise its pitch ever so slightly. It's called 'tuning to the attack' (in other words, how you 'attack' the strings).
Once you are satisified with the intonation, the next thing to do is make sure all of the strings are fully settled in and stable. This means you have to pull and stretch each one, re-tune up to pitch, and do the pulling and stretching again and again until you reach the point when you pull and stretch the string and it returns to pitch OK. You can still see live players re-tuning after every 2-3 songs. This tell me that they have not got their strings stable enough. Atmospheric conditions in the venue can play a small part, but the guitar(s) should have been well acclimatised before the gig started.
Also, check for any 'binding' in the nut. This is mainly on the top three strings. Bend the string above pitch as far as you can and let it return. If it does not return to pitch then it is likely binding in the nut (particularly if it stays slightly sharp). The string groove in the nut therefore needs to be widened - if you're not confident in doing it yourself, a competent luthier should be able to do this for you quite easily. You will definitely know when a string is binding in the nut groove when you hear the dreaded 'ping' as you bend the string!
Apologies for the long post, but I hope it helps you in some small way. Being an owl arse, I can bring 49 years of gigging experience to the table, and hope to help others with some of the knowledge I've acquired (from others) along the way! As Timothy Leary once said (about the only decent thing he ever said!): All part of the future, passed on from the past.