If things slip that much, you'll get quite a bit of frustration out of the character. My violin had a string that would always slip and go out of tune, sometimes just after tuning it. Now if it happens during a song, that can be really annoying. Can't always stop just to retune, and that would give need for knowing how to move his hands around to still be able to play and not sound horrible.
Get your pegs fitted again.
If you want to make it simple, but aggravating, have everything in a fixed state.
But have it tuned with scordatura.
Alternative/Cross tuning. I'm not sure what the common variants are for guitar. But for violin, which is typically tuned G/D/A/E, bottom to top, it isn't uncommon in some folk music traditions to raise the bottom two strings a note, ending up tuned at A/E/A/E. To give it a bit more resonance, and to make the fingerings symmetrical whether you're playing high or low. Or if a song is in D major, you might lower the top string a note, from an E to a D, to allow a constant D drone to be played easily and continuously.
Of course, if you're used to a particular tuning, you naturally finger each note for that particular tuning. Change the tuning, and your fingers will get all messed up!
Sometimes, the composer is trying to screw up your fingers. For example, in the 6th cello suite by Bach, the top string(an A) is tuned down(to a G), because the chords are practically unplayable with the standard tuning. But using an alternate tuning, it is playable, and sounds good.
Or, if you want to save yourself the trouble of having to understand and explain scordatura to a musically illiterate audience, just tune to a different baseline.
Generally speaking, in modern times, we tune to an A(Band people, shut up
). This A is defined to be the sound wave of 440 wavelengths per second.
However, historically, that A has ranged from 415 to 460. That's quite a difference, when half a wavelength/second is easily detectable by professional musicians! It's varied by region and ensemble as well. Eastern Europe tends to tune a bit sharper(higher) then Western Europe/US, for instance. So while the guitar might be perfectly in tune in Spain, it'll get more and more out of tune as the character makes their way to Turkey.
Continuing that theme, guitar isn't a standardized instrument at all. So different regions will build them to slightly different proportions(sometimes largely different), play with different techniques(Flamenco vs flat-pick vs jazz, etc), so the instrument might be regarded differently from place to place as well.
