My 15-year old Yamaha is not the world's best, but good enough. We've come to know each other over the years, and have learned to compensate for each other's shortcomings (the Yamaha has to work harder at that than I do!). If I tune it "un-capoed", I find that the thicker strings go a touch "up" on me as I put the capo on 3rd fret and above. So, as I use capo on 3rd, 4th and 5th fret a lot, I tune it "naked" first, then put the capo on 4th and adjust the tuning. With the new electronic tuners that does not take long - 30 seconds is enough for the lot.
But what really throws the tuning is temperature changes - they affect the Yamaha much more than my 6-strings. So before a gig I make sure the Yamaha is in the room and out of its case 30 mins before, to get acclimatised - then I tune it.
Someone I met last year had a Fender 12-string, and that seemed to be the the dog's knees or something like that - beautiful tone, and kept its tuning immaculately. But then, he bought it for $3,500, and I only paid $500 for mine!