iCloud Two-Factor Authentication
Since 15 June 2017, Apple requires that all third-party apps syncing with iCloud use app-specific passwords and this includes Contacts+.
To create an app-specific password:
1) Go to https://appleid.apple.com/ and sign in.
2) Scroll down to Security, then click 'Generate Password' under 'App-Specific Passwords'.
3) Create an app-specific password for Contacts+.
4) Copy and paste that password into the password field on Contacts+ Pro Settings section when you connect your iCloud account.
Please do check this video out for the step-by-step procedure:
For more information on two-factor authentication, please visit Apple's website.