It's always a sad day when I update my "scene missing" tag.Supposedly the lifetime of a web page is 100 days. I suspect Youtube videos have considerably accelerated decrepitude.
I mirror all of the the images that I post here instead of hotlinking them, but mirroring videos would be a lot more trouble.
Do you also get that thing where a YouTube video claiming to have been up since 2011 goes "poof" within a week of your linking to it? I do. Kind of makes me feel like God. Or at least Atropos.
You should build a mirror archive for the videos you are linking to. And when they go down you can upload them again (to youtube or whereever) and update your links.
Most of the time when they vanish from Youtube it's because of Content-ID or a copyright claim, so that wouldn't even work.