I've the very same problem since a few days ago ..
whenever I try to download some youtube videos it show me this message :

so whatever i enter in the "Username(BasicAuth)" field it will show me another window asking me for Password ?
i tried entering my own user name & pass of my youtube account without success !
and here is the youtube link as example (same link used in the previous pic )
**External links are only visible to Support Staff**www.youtube.com/watch?v=JUietR4a3MU
and here is JD Version :

I'm using Win 7 x86
Note :
I found out that it can grab the same link without asking for username & pass but after I did the following :
Tried to grab the links 1st time and he asked for username & pass then I clicked cancel then removed all the offline links & closed JD and reopened it and added the same link manually and it worked this time as JD grabbed the video without any problems …
But JD still asking me for user name & pass on videos that I try to download for 1st time and to download them I've to do the whole previous procedure to every single video !!