I can't unscrew the aerial on my Fiesta so that I can take it through the car wash. Every man and his dog has tried to remove it, using pliers, etc. but to no avail.
Seriously, if you def can't get it off and you must use those awful mechanical car washes all you can do is remove the whole thing (base and all) and fit a new one.
Incidentally have you tried spraying the joint between the aerial & the base with WD40 (penetrating fluid). Leave it for an hour or 2 then try again to unscrew it.