Try soaking the clasp in baby oil (or straight pharmaceutical mineral
oil) for a few hours, and see if that loosens up whatever is gunking
up the threads.
If that doesn’t work, try setting the half of the clasp most likely to
contain the male end of the threads on a zip-lock bag filled with
crushed ice. Don’t leave it there for long. This might cause that
half of the clasp to contract enough to allow the threads to work. Be
careful. Ivory doesn’t respond well to sudden temperature changes.
Once you have the clasp apart, inspect the threads for damage…and
then clean them thoroughly with mineral oil before rejoining the
I hope this works for you! Whatsoever thou doest, do gently.