A lot of the time this occurs from sliding tubs over the tape. The tape gets creased, bent, snagged if you may...then the tub wears away at the tape like an open wound every time you pull the tub in and out.
Thats why its a good idea to have a routed slot to run your heat tape along rather than allowing tubs to sits directly on top of the tape. This will help prevent the constant wear to the heat tape and more importantly reduce the risk of harming your animals or anyone else in the household.
Now is this the case with your situation...I don't know. Just reminded me of what I have encountered before and thought I would share.