If it is flexible adhesive it is probably a urethane adhesive. They are used in the flooring
and tile industries and easy enough to find in those departments of any hardware
store. If it is just a small strip, look for a product called "Goop" sold
in tubes (small and large) in blister cards at most hardware
stores and places that carry epoxy and the like. There are something like six varieties of it, plain "household goop" is the default choice.
But I'm not sure how well it sticks to itself, you might want to call them and check on that. I suspect you'll need to scrape and abrade the old stuff off, to get good adhesion for the new stuff.