Why does this keep happening?
 

For about a week as I am surfing QB, I get this plain white drop-down box with this message:

Authentication Required

The server https://client.projects.com443 requires a username and pasword. The server says Restricted.
then there is a space to log in

It only appears for a second, then gone again. As a matter of fact it is so quick that it took many viewings to write down the entire message.

I have not been able to figure out any particular thing that causes the drop-down to appear. I am logged into the board all the time.

Could it be a firewall protector (security)

General thought on the web is that it's one of the ads and google's adsense not behaving right on the site. If that's the case, there's nothing for you to do, it's an admin problem. I haven't seen it, but I run ad blockers.

Maybe your "security" is deleting it quicker than you can read it (once). I'd also be aware of funny looking URLs like the one you posted; and DO NOT open it! better safe than sorry.