Even I got this thing and was very frustrated. These are some reasons why you're getting 'the server is busy' thing:
1.You can only use Game Sync after 1 hour.This means that if you have used it once,you can use it again after 1 hour.Also you could try shutting down you 3ds and use Game Sync after restarting the 3ds.
2.The servers of PGL are always really busy so try using Game Sync after a 3 or 4 hours (or at 3 in the morning :P)
Hope I helped!