I've been using the "Clear Recent History\cache" solution for a while now, but I've noticed that it stopped working after one of firefox updates (probably 20.0.1). Because of that I've switched to https://addons.mozilla.org/en-US/firefox/addon/dns-cache/ add-on to do the DNS clearing. I hope this will help someone with the same problem.
Edit: Changed the url as suggested by Haozhun.
Edit2: Unfortunately as of FireFox 32, this plugin is no longer compatible and cannot be used. Possibly https://addons.mozilla.org/en-US/firefox/addon/dns-flusher/ might be able to replace it.