Chris, I had this happen on an old bug convertible a long time ago. The spring makes the hook pull on the little ratchet, and then pushed on it to release when we push the button. The pivot for the ratchet had worn enough that the ratchet could wiggle sideways and the hook would slip off the ratchet. I managed to shim it with copious amounts of swearing (it took several tries to get it to stay put). I know you said you didn't want to replace it, but only the handle needs replacing and it's stupid simple to do. I think all the bugs and things had exactly the same handle. The easy fix really is to swap it out for a new one like this for a whopping $28.49 LINK
Just undo the cable adjustment nuts, pull out the pivot pin for the whole handle, put the new handle in, swap over the cable attachments, re-adjust and then forget about it for the next 50 years. It'll take about 1/10 the time of getting the old part shimmed up so it doesn't slip because you have to take the handle off to do the shimming anyway. I had it off and on a bunch of times before I'd gotten a good fix. If I hadn't been a poor student (in both senses) I would have put on a new one.