Games that don't ask after hitting delete, don't have Game Center. So unless they have OpenFeint or Plus+ then your achievements won't be saved. Just the Game Center games ask if you want to keep the data.
im afriad this is wrong, games such as Agnry Birds Seasons and Real racing have game centre and i dont get the "remove data" option for these so i am stuck with them. any other ideas?
i'm afraid that apple will forbid the use of 3rd party social platform soon...openfeint and other platforms better find another place to go. now it seems Ngmoco is the only winner...
Try re-downloading them again again then go slowly when deleting it. Happened to me one, and I think it was because I happened to still have my thumb on the screen when I was deleting, and it registered the "Keep Gamecenter details" option. don't worry about re-purchasing... as long as its teh same itunes account, you won't be charged twice.