Not wanting to hijack your thread here, but 'strings going out of tune' can mean many things. Take for example my recent trip to South Africa where my niece (who plays piano and is learning guitar) asked me to take a look at her guitar. This is a 40 year old vintage Korean built classical guitar.
So first things first, check out the tuners.....perfect.
Ah, maybe the bridge is pulling up when being tuned.....check it and nope it stays dead level.
Hmmm...action is pretty good, nut needs replacing as it is a bit worn, but why would it be going out of tune so quickly......ADE, yep...was in tune, now completely out. Check the tuning on open strings....dang! Still in tune? No! Can't be.....could it?
I need a ruler, nut to the 12th fret 285mm, ok! So 12th fret to bridge we are expecting 288mm..........and it's only 280mm!!!!!!!!!!!!
Whoever built the guitar in Korea stuffed up. The bridge in 8mm to high up the neck and has NEVER played in tune its whole existence.
Easily solved, remove the bridge with steam, mark everything 8mm further down, reglue bridge with Titebond aliphatic glue and custon bridge clamps, finally redrill bridge pin holes. Too easy!!! Small problem.........man cave and tools are 10,000kms away in Perth and I'm in South Africa.