I have the same problem with maintaining friendships outside a particular activity where they initially developed. I'm not sure it's always as simple as "fake" friends versus "real" friends.
There was one group of friends where this was the case; sadly it took me several years and catching them out lying to me on more than one occasion to deliberately exclude me from events to figure this out.
But on the majority of occasions I think it is probably more likely that something was just "missing" from my ability to communicate social desire to them and, furthermore, inasmuch as they failed to maintain contact with me, I was equally guilty in that regard.
I think I also have a tendency to compartmentalise my life, including friendships, and wonder whether maybe other people do the same.
Or maybe relationships, like interests, simply wax and wane with time and as people move on into different life stages and different activities the relationships run their course.