A hammer?
OK, I had my fun. Take out the liners, the brass nails are driven through the wood and then ends are peened (flattened) to hold them in place, like a rivet. After awhile they loosen up from either the wood expanding and contracting from humidity changes as the interior wood is unsealed, or the top being flipped open and letting it bang into the rear of the case which pulls on the nail heads.
You can try to tighten them up by placing the heads against something solid to keep them from backing out, and then from the inside of the box, use a hammer and pin bunch to re-peen the ends tighter against the wood. The case wood is thin, go easy with the hammering.
The other alternative is to replace the nails with miniature brass wood screws.