If the detached lining is still in good shape, you could reattach it with flat head brass machine screws (with self-locking nuts) instead of rivets. Lots of big rig air brake linings were bolted to the brake shoes that way. It's possible the shop that did the reline job just didn't do a good job of riveting the linings on. You could also add some counterbored holes in the lining material between the existing ones and drill a corresponding hole in the brake shoe.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
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