I've heard that there's a new type of security in Facebook. When logging in they automatically check if the IP Address is similar to that of the original IP during registration. That's in order to prevent hacking into someone's account via the three methods i.e keylogging, phishing or social engineering.
So, since VPNs and proxies change your IP, Facebook might just think that you're intruding in someone's account. I haven't tried it (I will) but I hope it doesn't work :P. Is it possible?