I totally love git add -p and git stash but I occasionally have the following problem, which is reproduced by the following sequence of commands:
git add -p
git stash
git stash --keep-index preserves your index, but it still adds the index contents as part of the stash.
git stash --keep-index
Try git stash save -p -- a bit more tedious to save the stash, but will probably do what you want.
git stash save -p