I restrung my guitar 2 days ago (Dean Markley's Reg 10-46 I believe). Yesterday it was fine (except the strings didn't really stay in tune after I'd tuned up). Today I was tuning again. Low E to B are fine. High E refuses to tune. Eventually I get it right. I play the Chromatic Scale twice and then the string comes out of the tuning peg (didn't snap though). I put it back in, tighten it again, but before it gets to the point where it's playable, it loosens right up. Either I screwed up while restringing or there's something wrong with the string.

Is there a way to fix this, or do I need to buy a new string? And if so, would they sell me a High E string on its own, or can I just buy a single one on its own?
The tuner's one month old. It was tuning fine with the old strings. And I don't think the tuner is the reason that I can't use a 2 day old string.
and you don't seem to have a floyd so that can't be the problem. i guess it'sa either in your bridge or indeed the string. new strings have to stretch up, so they're never in tune at the start. i say replace the string see how it goes and if not take it to a tech, or if you know what your doing take it apart yourself.
Wise Man Says: The guitar is obviously female, she's got hips, breasts... and a hole.
UG's Flamenco Club
then the string comes out of the tuning peg

It sound like your string is slipping, which can happen with the thinner strings, as they got no winding like to low ones.
Try to double-wind the high E (put it through the tuner, around and through again).
Jackson DKMGFFˑˑˑˑˑˑˑˑˑˑRandall RG100SC G2
Washburn DIME 333ˑˑˑˑˑˑˑRandall RH200X / RA412 2x Half-Stacks
Dean From Hell CFH
Ah, can't even get the string to stay in now. I think I may have cut it too soon or cut it too short or whatever. Guess I'll just buy a new one tomorrow.