Password Expiration Warning Message, not being prompted for a few Notes users, though the password was expired on their Notes ID files.
In this specific case, this customer has a security policy enabled for all the Notes users, which sets them to change the password every 30 days. The customer has not enabled the Password Expiration on the SmartCloud Notes Administration: Administration--->Manage Organisation ---->Lotus Notes--->Account Settings on the Navigation Pane ---->Password Expiration.
Resolving the problem
Enabling a warning period without enabling password expiration produces unexpected results and is not supported. Customer should follow the procedure documented on the below wiki, to get the password expiration warning message as expected.