How to keep cream cheese from molding?

After 45 years of cooking & housekeeping, I still have questions. 
How do you keep cream cheese from molding?  When I use 1/2 an 8-oz pkg, I wrap the other half in saran wrap and put it in a sealed plastic container and refrigerate it. Within a few days, it is moldy on the cut edge, under the plastic wrap.
I have tried everything and searched for an answer to no avail. I sure hope you have an answer for me.
It may be possible, that you can’t keep it from molding but I would like to know.
 
I really enjoy ALL of your advise in my local newspaper, Constitution-Tribune in Chillicothe, Missouri Please respond. Thank you