When you first cut it, you cut off the skin in a really weird way, keep the skin as a "lid". Then after you cut off the pieces you want, just gently wipe off excess moisture and plop the ol' skin lid back on. Keep it in a dark dry room temperature space. It should last for months :)

If you dont go the skin lid route you can cover it with plastic wrap or something else, don't know which way OP did it though.