I had this happen with some rubber coated binoculars, and could never completely remove the tacky though. It would clean up for a while but always came back fairly quickly, so I guess the rubber was breaking down.
It is certainly the material itself. Common problem with lots and lots and lots of types of plastic'y materials. I'd try using simply using some soap and water and see if that helped first, if that didn't work, I'd escalate to very fine sandpaper. (My favorite plastic problem is a kind of plastic which is very common in folders and binders which react with laser printer pigment, removing it from paper and adhering to the binder instead. Binders which destroy printouts... genius... (And that's why I stick to cardboard or extra cover sheets when it comes to storing paper documents.))Edit: Basically what the Sea Monster said, I guess.
Send it to me and I'll live with it