It is probably firefox caching basic authentication information. You can verify that by looking into HTTP traffic - you should see that GET requests containing Authorization header. Try to restart firefox or Clear Recent History->Active Logins .
Thank you for your response. Yes, it was the Firefox cache and doing Clear Recent History from the main menu did the trick. However, there is also a button in the Firefox toolbar named "Empty your cache". Using it doesn't help. Probably a Firefox bug. Notice also that restarting Firefox, or the EAP server, or undeploy/deploy, or all this, doesn't change anything neither.