I can only confirm what ballskicker and Shadow said - I’d remove the old caulk both mechanically and with the help of a solvent and then caulk it back in.

However, I’m also pretty sure it will eventually sag again without the help of a retaining mechanism.

Given the pictures you posted (which might not provide the full context), I assume someone really just caulked a glass panel into the profiles and left it at that. I assume you would like to avoid drilling the glass (can be done, but is tricky and has the potential to create a mess pretty quickly), so I’d simply manufacture a retaining cap that closes off the profile and holds the glass panel in place. I’d drill a hole into the ceiling to hold the cap in place, or into the profile, depending on the material and the remaining situation at hand.

I’m talking about mounting that right here, after sliding the glass back in / caulking, of couse: Image