why are you using a wrap in the first place? it deadens the vibrations of fish bites.
i use only 13 fishing wicked rods (19"UL) to get the most vibrations from a rod and get the fastest hook sets too. also, i use frabill titanium strike indicators so i can watch them breathing on my jigs.
from the sounds of it, you used a cork wrap? and then watched it blow away?
i have used reel wrap on open water rods on game fish rods that have small handles and make your hands sweat. sweat isn't a problem on ice tho and the fish aren't game fish.
maybe i don't understand if it's a question or comment.