Your heavy-duty industrial tape might be incredible, but so is Garmin's rubber sleeve. I have heard reports of some tapes sticking to the rubber, but have never seen a successful fastening using tape myself.
As for oil dissolving the glue, it might be true but I do not think this is the sole reason. Never handled my GPS with noticeably greasy or oily hands, so if it is from that, it's natural skin oils that cause it.
Anyway - there are no ways around this or excuses for Garmin, a GPS sold as a "rugged" outdoor device which can not handle "standard use" - a little heat or fats - without breaking is FAULTY FAULTY FAULTY.