01 convertible and the weatherstripping on the drivers side that runs along the front half of the window keeps coming loose and I press it back into place and then 2-3 times later, when the top is closing it will drop back down.
Would it be alright to use weatherstripping glue to hold it in place or is there something else I can do to prevent this from happening again?

 

it probably is really dry, you should get some Gummi Pflege Stift (rubber care stick) and give the entire weatherstrip a couple good coats of it, get into the cracks and around the grooves where it fits into the hood rail. It may expand enough to stay put AND never need anything else. It also helps keep the window seals tight...squishy is better.