Front Door Weatherstripping Loose

Both my front doors have weatherstripping that runs vertically near the hing that has just pulled completely away from the door itself. It is "loosely" hanging in there, and doesn't seem like it can fall out, but it obviously isn't doing the sealing job it's meant to. Any suggestions on what the best kind of adhesive could be to put it back on the door without having to take the door off? I've tried trim double sided tape (which didn't stick to the rubber) and some black silicone (which wasn't immediately tacky enough to keep the rubber in place, and it's impossible to clamp or even hold it in place for very long. I need a glue that's immediately sticky. So, I was thinking of contact cement, but worried that would be rigid.