It was hyped in 2010 by Facebook founder Mark Zuckerberg as "next generation messaging" but after 3 years, the service has seen little use by users who opted to continue using their established email system.
On Monday, Facebook announced they will be phasing out the service by March 2014. A Facebook spokesman said
Over the next few weeks we’re notifying people who use their @facebook.com email that the feature is changing. When someone sends you an email to your @facebook.com address, it will no longer go to your Messages on Facebook. Instead, the email will be forwarded to the primary email address on your account. (People will have the option to turn forwarding off.)
We’re making this change because most people haven’t been using their Facebook email address, and we can focus on improving our mobile messaging experience for everyone.