All I can do is guess, but I would guess that either the tapes adhesive is too wimpy or it may be reacting with something in the Goo that makes it lose adhesion over time. :dontknow:
Another thing that will make the glue on the back of pretty much any tape soften is heat. How hot is it by your screen?
How hard did you push the tape onto the screen? You should have used a tool similar to this one (know as a "J Roller") to evenly push the back of the tape into contact with the screen.
It would also be a good idea to take some coarse sandpaper and scuff up the paint where the tape will be applied; this will create little valleys for the tape adhesive to go into.
There is an old saying in woodworking that you should NEVER depend on glue alone to hold something together, that is why there are so many different types of joints and mechanical fasteners for the carpenter/cabinet maker to choose from. Glues have gotten better over the years, but it's still a good idea not to depend on glue alone. The exception to that rule is contact cement, but only if it's used properly.