Question

Why authorization is requested every time when sending the text to Evernote?

Answer

You are logged in to your Evernote account from within ABBYY TextGrabber. When you attempt to send a note to Evernote, however, the program asks you to log in again. 

For greater security, the program does not store your authentication data. It only stores the key returned by Evernote when you log in. This key is only valid for a limited period of time. If Evernote asks you to log in again, this means that the key has expired. This is the expected behavior.