For a long time, now I have no issues connecting to the web UI. Day after day, month after month, successfully connected and logged in every time I tried. I have not updated my firmware as I assumed, everything is now working, why tempt fate. My router settings remained constant throughout. 

I discovered that the internet time server (ntp sever) I have been using on my devices has ceased to exist and no longer works. In fact, the service was suspended a long time ago and I never noticed - how often does one check the date/time in their router? After updating router config setting to a new ntp server, almost immediately my ability to connect to the C9 web UI began to fail again. Since the only setting change I have made in a long time was the timer server, that is the problem. 

Reboot the router, quickly login to the web UI and delete the time server address(s) then save the settings so that the two time server fields are blank. Set the time on the router manually or by hitting "get GMNT time" button with the server fields empty.

I don't know why this causes the Web UI connection problem, I don't know if a firmware version more recent than the one I am using addresses this issue, but this is how to fix the issue if you have to reboot your router every time you wish to enter the Web UI to make any settings changes.