The behavior about requests taking a long time and then showing a Windows authentication dialog sometimes suggests that the IIS worker process that hosts WebLink has crashed and restarted.  If you have access to the server machine, you can just watch process monitor while you reproduce the problem.  If you see a w3wp.exe process disappear and a new one come back (with a different process id), that's what's happening.  In this case, it's not going to be something you can fix yourself; you should go through your VAR to open a support case.  Support will want a crash dump, so if you know how to take one you can get a head start on that.

If it's not a process crash, I'd want to see a trace of the browser requests from a tool like Fiddler to get a better idea of what is causing the credentials prompt.  Those contain all of the data that goes back and forth between your browser and WebLink, and your screenshots make it look like your information is potentially sensitive.  If you can share the data on a public forum like this, go ahead and attach the trace, otherwise you'll want to go through support.

All that said, I was just looking through some closed issues and there was a similar report filed against WebLink 8.  That issue was resolved in WebLink 9, which I don't believe you have ugraded to yet.