Store the Access Token as it's returned and reuse it

From https://developers.facebook.com/roadmap/completed-changes/#december-2012 :

New security restrictions for OAuth authorization codes
We will only allow authorization codes to be exchanged for access tokens once
and will require that they be exchanged for an access token within 10 minutes
of their creation. This is in line with the OAuth 2.0 Spec which from the start
has stated that "authorization codes MUST be short lived and single use". For
more information, check out our Authentication documentation.