Tweaking deployment clasp

I got a - superficially - Tag leather strap with a deployant clasp. For whatever reason the adjustable end can't be pinched tightly enough to stay in place, and over time slides out...



Is this mechanism intrinsically flawed or can I do something about with some pliers, or plump up the leather, or get a different clasp that miraculously works better?

TH makes deployant clasps for 2mm-thick straps and for 3mm-thick straps, depending on the watch model. If that's an aftermarket strap, maybe it's meant for a 2mm clasp but you have a clasp for 3mm straps.

Any aftermarket straps for TH watches and the factory deployant clasp should list the strap thickness. Perhaps you can get a strap that has 3mm thick ends.