Hi Mark! Thank you for posting to Perfect Swing - Golf official forum site. We are very sorry to hear that you haven't been invited to any Special Stages. There are many ways to get invited to; you can be invited by friends; when one of your friends has been invited to Special Stage, they will automatically be sent an invite to your character as well. You can also purchase a Special Stage invitation to the shop by going to the Shop then tap the SS tab. In there, you can select what kind of invitation of Special Stage you like. Last is from Fever mode. In Fever mode, you will be playing using double, triple, or more stamina to enter any stage of Career mode if you have at least one gold star to a specific stage. In Fever mode has also a high chance to trigger the Special Stage invitation from a certain stage, however, make sure that you have completed all the Black tees of all the courses in order for you to play them Special Stages.
We hope this helps, if there will be other questions please let us know by replying to this thread or message us privately by sending a ticket.
Mark D'urso