That is because Apple are now insisting you provide an “App specific password” that you have to generate by logging into your icloud account and creating one. So without realising it and me.com emails are not accepting your password, even though you know the password is correct. In a recent upgrade, Apple decided to increase the security of your (also me.com) email accounts, not when using Apple mail but when using Microsoft Outlook for Mac (Office 365) or other mail apps. Has Outlook stopped accessing your or me.com emails?
