Here's what I would do (aside from avoiding sequins in the future -- I rarely if ever see them used on competition dresses):

1) Keep unravelling the end of the thread and pulling off the sequins until the end is long enough that you can thread a needle and sew the end back into the dress, knotting it off so it doesn't unravel any more.

2) Glue the sequins you pulled off back into their original places, sans thread, using a good smooth-to-fabric glue like Gem Tac or E-6000.