Tying a knot using elastic string.

You might try a simple knot combined with a burning the string to make it bond with itself.

@bodyhead, that’s basically what my husband suggested. I’ve got three bracelets so this may be the only solution.

What about a crimp bead over the knot?
Plus it would hide it quite nicely.

A little dot of glue in the knot might help, too.

Hot glue would probably be the best type for a long time hold.

Thanks to all who tried to help. I actually used clear nail polish after tying the knot. It appears to have worked.