Gmail considers regular email programs and backup programs (i.e Hotter, Outlook, etc.) to be "less secure", so in order for them to get access into your account, your "Allow less secure apps" option must be turned on.
1. Turning on 'less secure apps' settings as mail domain Administrator
Go to settings for less secure apps.
Enforce access to less secure apps for all usersradio button.
Allow users to manage their access to less secure apps, but don't forget to turn on the less secure apps option in users settings then!)
2. Turning on 'less secure apps' settings as mailbox user
Turn on access.