Our "Manx", Pixie, (she's technically a randombred DSH, but to us, she looks like she could have been a show quality Manx, if only she were pedigreed

) has a very similar problem. As long as we've had her, she hasn't had any recurring litterbox issues other than these small deposits just outside of the box. I can tell that this is entirely accidental on Pixie's part, because she always notices it as soon as it happens and attempts to bury it. Since carpet isn't real good for burying poo, I always quickly run to her rescue with some toilet paper and dispose of it for her.
Pixie has come from a long line of randombred "Manx" cats that have been with my mother-in-law's family for generations, and pretty much all of the rumpy cats (well, those few who were inside cats and litter box trained at all) have had this problem.
The way that I understand it, and this may not be entirely accurate, is that the "Manx gene" causes an abnormal shortening of the spine, which often leads to decreased sensitivity in the hind area, especially in rumpy, or completely tailess cats. Because of this, they have a harder time telling when they are "done", and will end up inadvertantly dropping some excrement over the side of the box when they are burying or as they are leaving.
I don't really know if there is anything that can be done about this, since it seems to be tied in with the major distinctive trait of the Manx. We also have never really tried to correct it, as it has never been much of a problem for us. However, you should should probably talk to your vet about it, especially this seems to have noticeably increased in frequency lately, just to be safe.