I know that I can select Amazon Prime in the advanced settings. Even if I do NOT select this and run the CCleaner, I have to log in again completely in the Amazon Prime app (Win 10). This is a bug for me!
Are you using healthcheck or custom clean?
i had the same problem and invest hours to find out why....on the first page Windows" at the "Internet Explorer" menu the options COOKIES store the account data from amazon app. if you deselect it then you will not be logged out!