Chris, The first thing that springs to mind (sorry - couldn't resist
the pun) is to switch from the supplied square silver wires to the
same size/shape wires in nickle. It is a much harder metal, and
won't be as susceptible to wear, bending, and breakage.
Another possible solution (but it's more work) would be to insert
silver tubing into the rivet area, then thread the rivet wire through
the tubing to make more of a hinge. It's kind of difficult to
describe without graphics, but you would, in essence "line" the area
with tubing, in which the rivet can move freely. As with the other
solution, it would require changing the wire supplied, but it
eliminates the problem of rubbing points on the wire, which may
increase its durability.
You don't say how the cufflinks are falling apart, though, which
could provide more clues. Is a rivet head falling off and the bar
falling out? Is the bar breaking somewhere on the inside of the
joint? or what?