Rivetted scales get loose all the time; the main culprits are trauma and warping/expanding/shrinking of the fibrous organnic grip material from moisture exchange (mostly with the air). This type of sword tends to have a short (ie not full length) flat tang that may or may not be full width, rivetted to a plate that is soldered to the tangband. An arrangement like this seems more liable to wiggling than a true flat tang. If you don't want to tighten the rivets (and the holes may be wallowed out; one sure looks it, which complicates this) I suppose you might explore if you can do any good with wedges, shims, or injected adhesive/filler of some sort.
M Carter; what kind of pitch do you start with, and where do you get it, please
To the side, I have seen the pitch inside a tulwar handle be stabilized re-bar style with a matrix of wiggly copper wire.
Is a false edge that is not "dropped" (ie widened) a yelman? I have always heard and read the term yelman in association with the dropped edge.