Ok, I see — on the “IPs that are Locked Out from Login” tab, IPs are only added automatically to that list when a visitor breaks a rule. You can only block IPs that are already listed there when they appear, but the “Manually block IP” button above that will only add IPs to the first tab, “IPs that are blocked from accessing the site” no matter which tab you are on.
For being unable to block from the Live Traffic view — can you try blocking one on that page too, and see if anything appears in the javascript console? These blocks are temporary, so if you want them to be permanent, you would have to go to the Blocked IPs page shortly after, and click the “make permanent” link.
The 404 error in the screenshot is helpful, but shouldn’t cause this problem (it’s from trying to get a flag image for a blocked IP that has no country listed), so I will put in a separate bug report for that. Thanks!
-Matt R