We had that happen a few years ago and it is the slot in the plate that the pin engages in which becomes worn and under tension the pin can spring up and out of the slot.
We engineered a thin plate to bolt to the existing plate and thus create a new slot over the existing one. That seems to have worked quite well.
Our pin wasn't worn at all, only the plate.
Our furler is slightly different to yours, but the principle is the same.
You need to take the two halves of the top piece apart to get access to the plate and the pin.
Our pin was held in by a nut underneath the top piece. Yours may be different.