WGT knows two types of friend invite:
- invite friends by mail to join the game via the big "INVITE" button on the left,
- invite players who are in the game to get on your friends list (see tab on the left).
A successful mail invitation should automatically put you on each other's friends list, so either this didn't work or one of you terminated the friendship. You may look up the name in the community/players tab and press "add as a friend", or use the "+" sign at his name during a common game. He'll have to accept the invitation ("invites" flashing blue) before the friendship will be installed.