On my own profile it says: "Melody Regular 2013 Visit Melody's Cottage up until December 25th, 2013. You do not have this achievement!"

...

When I visit my achievement page, the 25 mark is green. I didn't receive the prize though.

It's probably something small, but I'm not sure what's going on.

have you missed a day?

I think maybe the counter is glitched or something? You're missing two days, if those were from before the 25th then your achievement shouldn't be green but since you are over 25 days, maybe that's why it turned green? I would file a ticket, they can find out if you're supposed to have it or not and remove it if needed or give you the prize if you weren't awarded it and should have been.