This issue can be caused by an extension or plugin that isn't working properly.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of the add-ons is causing the problem (switch to the DEFAULT theme: Tools > Add-ons > Themes).

• Don't make any changes on the Safe mode start window.

See:

• Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems
• Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems

I had a similar problem, just that switching away from the tab and back did not update the address bar neither. I found out it had something to do with the add-on IE Tab Plus. A different discussion on Tech Support Guy came to the same conclusion. Updating the add-on solved the problem.