This will work for awhile, as well as cleaning with warm water and dish soap. But nothing will help if the grip is oxidized and destroyed by UV ray.
Except for those grips with a thin wrapping on top ( Winn grip and the similarly constructed ). Grips should last more than a season if taken care of.
The longest period I had the same grip on a set of irons was the old Royal Grip ( Royal was bought out by Lamkin Grip, I believe ). The set was a tour wrap and it last more than a decade with active use. By the time I replaced them, it was still tacky but easily peels apart once I split the end. Constructed mostly with rubber compound if not all of it.
I believe the older model Star Grip wrap is of similar construction.