If this is a regular problem, it might be caused by an internal error of the application. To fix it, try before logging off or shutting down the computer, to close the application. To do close the No-IP DUC program, you need to maximize it, go to File > Exit. If the application is started, you would find it next to the system clock.
It's advised to keep all your application up-to-date because in the latest updates, some errors like this one might be fixed. If you still experience problem with the program, try contacting the developer on the official website.