I assume you've tried restarting the computer.
We have not had any other similar issue so I'm wondering if something is wrong with your system.
There is an easy way to test that: go to your computer System Prefernces > Users and Groups > create a new user
Logout from your current user and login the new user.
If iReal Pro works there something screwed up in your user account.
If it works you can import the songs from the forums and then make a backup in .irb format that you should be able to open in iReal Pro in your normal user account.