I hate two face tape for this reason. It does not work under extreme conditions - heat, cold dry, wet - or if it has to hold any weight AND should not be relied on for uses in external areas. I don't even like using it indoors. The glue can dry out over time and I have found the thing I used it with sitting on the floor some time later.
Ray has the right idea to back it up with silicon, but make sure it's exterior grade silicone sealant/adhesive (note the adhesive part) or you'll just have the same problem again.
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