Edit the audio, select the Edit tab, position the play head at the end, then click the red record button. Record a few seconds of just background noise. Reduce the volume so that it's not audible. Save and close the audio editor. It should extend the audio track (and the timeline if it's longer than the timeline) to allow for the extra inaudible audio. And the closed captioning should stay up as long as the audio track plays.
I tried adding silence at the end of the audio track, but Captivate removes it automatically, so it needs to have some audio, not silence.