Put it through a car wash. That'll make it come down. But seriously, some on this site have suggested some sort of grease product, as you mentioned.
Also, you might have a bent antenna "mast," which isn't a big deal to replace.
I got fed up with mine and replaced it with a regular antenna from another contique at the junkyard. I had to take out the motor and everything, but all the attachment points are the same.
Just from the past year I've owned my CSVT, I've come to realize that they are just a little fussy when it gets really cold out. Maybe it's their European heritage.