FWIW, I have a Safari extension that allows YouTube video downloading. Over the last week or so, it's been a little hit-and-miss. It's usually very reliable, so I'm wondering if YouTube has changed something that makes the extension buggy.
I don't know if it's related to your downloading trouble or not, but I thought it was worth mentioning.
P.S. I tried two separate extensions, and both are suffering from the same problems.