Intuitively, I feel that it would only be possible to go flat, but I'll tune my bass perfectly, then later on when retuning, I'll notice everything is ever so slightly sharp. How?!
Quit playing in meatlockers.
If the strings get cold, they shrink a bit and go sharp. As they warm up, they relax a bit, going slightly flat.
Maybe your hands are cold.
This brings up those people who swear their basses NEVER go out of tune. For that to happen, they more than likely live in a temperature and humidity controlled terrarium. Actual, I might be speaking out my rectal orifice there about humidity.
Having lived in single digit humidity, playing gigs in Redondo and Huntington Beach, and other gigs in Twentynine Palms, I've NEVER had dampness or lack of it cause me any grief and cause any of my gear go wonky on me.
I may not have been able to breathe through my nose, even as substantial as it may be, but dampness at the beach has never caused me a moment's problem.
Your problem is some other dynamic I bet. It AIN'T the tuners as they don't slip, at least not to get tighter.
BTW - since moving to Montana where there is very little humidity in almost all seasons, I've STILL to have to need to adjust one of my over 20 truss rods. I anxiously await the day when I can use my Allen wrenches to make that adjustment.
[/soapbox] I just feel snippy today.