Instead, the launch pop-up disappears and the Play button becomes active again.
To try and resolve this issue, delete the cache folder, by default located in: C:\Program Files (x86)\Ubisoft\Ubisoft Game Launcher.
We would suggest creating a backup of the folder before deleting it.
If the issue persists, please reinstall Uplay.
Do not hesitate to let us know if you have any other questions.