There are several reasons that people have problems logging into VPOP3's services.
The most important diagnostic tool for troubleshooting these problems is the SECURITY.LOG file which is stored in the VPOP3 logging folder on disk. It can also be accessed in Settings -> Diagnostics by pressing the View SECURITY.LOG button. The SECURITY.LOG file will contain more information than errors returned to the user, because the errors returned are deliberately generic to avoid giving information to an attacker - for instance, if you tell an attacker that a username is unknown, it tells them they should try another username instead of attempting another password.
The most common, by far, is that they are using incorrect login details - ie an incorrect username or password. (The username is sometimes called the login name, or account name or similar).
The username is the name specified in the Users list in VPOP3. It is not the email address or a 'similar' name. So, if the name in the Users list is "robert", using "firstname.lastname@example.org" or "bob" will not work! Usernames are not case sensitive.
The password is exactly the password specified for the user in VPOP3. Passwords are case sensitive.
Each VPOP3 service has Access Restrictions which tell VPOP3 which users can access the service from which IP addresses. Make sure these are set correctly.
Each VPOP3 user has permissions which allow them to use certain VPOP3 services, for instance users could have their SMTP service access blocked in their user settings.