What kind of pumpkin is it? If it is a c. maxima type, their stems usually do rot away. If is is a regular Halloween pumpkin, the pumpkin may have turned orange before the stem was hardened. If you grew it yourself, remember that pumpkins need to sit in the sun for a week or so to harden. You don't want to keep the stem wet, even with a bleach solution. You want it to dry out before it can rot. Dry = no rot. Try putting it in front of a fan for air circulation, and maybe it will dry out for you.

Good luck!