It is undoubtedly because you have more than 20 friends and, in their infinite 'couldn't-care-lessiness', wgt limits you to 20 friends showing on your country club page. And they 'accidentally' removed the "Invite to Country Club" button from your friend's player profile page so you can't invite him that way either. A week ago, they said that would be fixed 'asap' and I am still trying to get them to define 'asap'.
Good luck! I know how frustrating it is to tell someone to stand by for an invitation and then not be able to send one!!