Try restarting the Viber desktop client, because it might be stuck. These things happen from time to time, but if the restart won't help, then reinstall the application. Wipe it completely from your PC and then install it again.
Use the following page to download the installation package: http://www.viber.com/en/products/windows
Don't worry about the messages, because they're synced to the cloud/phone and when you re-login, you'll see them in the desktop version.
