This typically happens if the SendSafely configuration has become corrupted. To reset the plug-in preferences file and generate a new, clean configuration file, perform the following steps.
Close Outlook, then go to "Start Menu -> Run" and type the following command: %appdata%\SendSafely
A Windows Explorer window should open the SendSafely configuration folder (if that doesn't work, the full path to navigate to the folder is usually C:\Users\<Username>\AppData\Roaming). You should see a sub folder named "SendSafely". Delete the entire folder and then re-launch Outlook.
This will reset the plugin preferences file, and a new configuration file should get generated when you re-launch Outlook. The SendSafely plug-in should then prompt you to re-enter your username and password.