Store cold porcelain paste in an airtight bag or tightly wrapped in plastic. Sometimes I do both...wrap in plastic first and then in an airtight bag!
Try using a product that sucks air out of plastic bags. Ziploc makes an inexpensive one. There's some new ones on the market too that might work even better.
There's some new, latching plastic food storage bins on the market. Small ones are inexpensive and claim to be airtight. Made by Sterlite...the type with a rubber gasket to help seal. I bought some and really like the way they latch.
Do not store really damp CP for a long period of time, this could make the paste moldy.
Store CP paste in a dry area at room temperature. Do not refrigerate, but you can freeze.
Paste that has been tinted with color will dry out faster than non-colored paste.
Don't store different colored paste in the same container if they could touch each other and transfer color. Wrap separately in plastic wrap first.
Please comment if you have some storage tips to share! ;-)