That's the best explanation I can think of. You tune up to pitch, but the string sticks in the nut a little; after a while, the excess tension between nut and tuner pulls the string a little tighter.
A little careful filing might work wonders. Alternatively, tune up, then press on the string between nut and tuner to help pull it through the slot, then give a nice tug on the playing length (about as hard as you'd hit it) to even things out. I'm in the habit of doing this, even though my slots are very carefully fitted.
The only other thing I can imagine is that maybe your neck straightens out a little after playing, either because you pull on it a lot, or maybe from the warmth of your hand. I think that's a real stretch (of the imagination), and don't see why it would be more obvious on the low strings.