Hello both. Thank you for taking the time to reply. Re PinkElephant's reply I have done as you suggested, on my iMac, deleting the EN password in Safari > Preferences > Passwords then went to Launchpad > Search (entered Keychain) > Passwords and deleted Evernote. Then I rebooted the iMac and clicked the EN icon in the dock, put in my login name/password and opened EN without a problem. I'm still learning my way around Apple stuff so please forgive me if this is a long winded reply of thanks.
I do leave the iMac logged in to EN, making notes on EN whilst using an iPad. However, I also have EN on the iPad if I need to use the iPhone in place of the iPad with the iPad in place of the iMac if I've no access to the iMac. It has been this way for several years without a problem.
Regarding the reply from RobertJLee I have to admit ignorance on your comment as I have no idea what Cloud Outliner Pro might be, never having heard of it. Am I missing the best thing since sliced bread?
Thank you so much for your replies. I await to see if the dialog box suddenly appears again!
Thanks.