Full Disclosure: I am the lead developer on the site I'm mentioning...
If you can get the URL to the .FLV file (just google 'how to get FLV URL youtube'), Upload by Transfer is what we call it. That feature gets released next week on our platform (see blog post for details). You provide the URL to the FLV, and the cloud service pulls it off and transcodes it.
Edit: Just tried this with the KeepVid suggestion in another answer. Just picked a popular YouTube video... http://play.nimbushd.com/view/lfsv
This is normally meant for production shops with automated workflows (HTTP/FTP servers) but FLV is supported and it's no different. And in the interest of neutrality I suppose you could also do this with encoding.com if you had a destination for it (an FTP server or something).
If you're not looking for a cloud service/hosted platform, then of course there are YouTube downloaders and you can just save the .FLV files off to your hard drive.
First, let me just say that this has not happened to me, and therefore I only know from troubleshooting other issues with people, but this is the most common answer.
What you're going to need to do, is access your YouTube account by signing in, of course.
Next, you will want to go to "account privacy". This will take you to your YouTube Privacy settings. (If not, log in first.)
Then, just look over your selected options. The issue may be apparent just by reviewing your settings, but if you can't figure it out still, be sure to make sure, first and foremost, that the box labelled Make Comments Private (or something of an equivalent meaning) is not checked.
For future reference, please make sure to check all of your settings regardless of what you may think they are set to. There is an extremely high chance that it is something as simple as one or two check boxes!
Best Answer
It is possible to programmatically remove comments, see this answer at Stack Overflow: "Remove a comment using the youtube data api v3?", but the quota will limit you to ~200/day.
Here is their help:
https://developers.google.com/youtube/v3/docs/comments/list https://developers.google.com/youtube/v3/docs/comments/delete
You can also go to this webpage: https://www.youtube.com/feed/history/comment_history and manually delete the ones you want, as many as you want, fairly quickly (and likely more than 10/minute, if you have patience).