Most all of the low cost screwless vises and essentially all the tiny ones have a pretty poor method of letting the screw pivot. I have a medium sized one and a small one and they both needed an upgrade.
Both just had a socket head cap screw with a rounded base on the head, something like a flat head screw. With just a few uses the screw mangles itself turning in a slotted cavity.
The solution is to fabricate a hemispherical washer and use a regular socket head cap screw.
In the photo you can see my smallest vise with the original screw assembly (on bottom, black oxide) which had the additional problem of rotating when loose so it wouldn't lock in. Above the original screw assembly is my new assembly. The hemispherical washer was made from drill rod on my lathe with a ball turning attachment. The nut assembly was made on the mill and belt sander and is sized to just fit in the slot so it can't twist. The new pin is a through hardened dowel pin.
Yes, the picture doesn't show a socket head screw, I didn't have the right one when I took the picture. I've since put the correct screw in.
I've been using this for a while now and there are no more problems.
The holes in the workbench are NOT from me, I got this well used.