We tested the combination of JetPack and our plugin on a live site and did not find any issues. Perhaps you can answer the following questions:
What's your site URL?
What version of WordPress are you using?
What version of the YouTube plugin are you using?
What settings have you checked in the YouTube plugin?
Please give an example embed code/link you pasted into your editor, for a video that disappeared.
When you say "disappear", is there anything there at all? A blank area? Or, just the embed link? Or something else? A before/after screenshot would help a lot.
Which Jetpack items have you activated?