OS X 10.10 (Yosemite) and 10.9 (Mavericks) will cause Final Draft 8.0.1 to prompt you to activate every time it's opened even though it was successfully activated previously.
To fix this issue, download and install version 184.108.40.206. It will overwrite your existing installation and once it's installed, you should be able to activate and run Final Draft without further problems.
You can download the 220.127.116.11 installer HERE.
If you receive a message that you are out of activations, contact activation support via chat, email, or phone at 818-789-6281.