Try the Firefox SafeMode to see how it works there.
A troubleshooting mode, which disables most Add-ons.
(If you're not using it, switch to the Default Theme.)

• You can open the Firefox 4/5/6/7 SafeMode by holding the Shft key when you use the Firefox desktop or Start menu shortcut.
• Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.
  

Don't select anything right now, just use "Continue in SafeMode."

To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut (without the Shft key) to open it again.

If it is good in the Firefox SafeMode, your problem is probably caused by an extension, and you need to figure out which one.
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes

When you figure out what is causing that, please let us know. It might help other user's who have that problem.

The problem is that this behavior comes during the session. If I restart the browser, it is fine, but then after some time the problems starts. Could it be that visiting certain web sites triggers this behavior?

I've used the current selection of theme and extensions without any problem for a long time. The only change I have done recently is to install a Skype extension, so the first thing I did was to uninstall it, but that did not help. I ran a full virus scan, and found some minor Java problems, but fixing that did not improve it either.

I will try to monitor carefully exactly when this behavior starts.

Thanks!

Maybe try to disable IE Tab as a test.