That is a tricky one!
You could try a manual logout from the Meraki dashboard, rather than just quitting the browser. This will hopefully destroy or invalidate some of the cookies used for tracking your session.
When using Chrome, you could try a CTRL-SHIFT-I to start the Chrome developer tools, click on the Network tab, and then click the "Test" button. Look for things coloured red - indicating an error. This is a real long shot, but it may reveal some additional useful information.
Do you have anything that does web filtering or checks your web browsing? If so, try disabling then during a brief test to isolate the issue further.
If you connect using a different Internet circuit (such as a hotspot) does the issue still happen? Perhaps it is something in the environment where the computer is located causing the issue. This test will help isolate that.