Help! Podcast has been on iTunes for years, but has just disappeared.

I can see no obvious reason why it should have been removed. There appear to be no technical problems; I haven't listened to any of it but I assume that the episodes contain no strong or sexual language - if they do you must flag them as 'explicit'. You could try contacting Support, though I can't promise how helpful they will be. Go to https://itunespodcasts.zendesk.com/hc/en-us/requests/new and click the disclosure triangle at the right of the 'Choose a topic' field - choose 'Re-activate Feed' and proceed from there.

This method of contacting Support is new, and I can't really say how it will proceed, but I would have thought that they would contact you again as you have had a response. If you can bear to wait it out I should see what they can do - if all else fails you can try re-submitting though you may fall over a bug in the system which will tell you that the feed has already been submitted; to get round that you would have to change the title slightly.