There could be a couple of reasons for this:
Make sure you are using the correct ports and settings. You should be using port 465 for SMTP, with SSL enabled. The SSL type, if you can select it, should be "Alternate Port" rather than "STARTTLS".
You may be trying to log in to the wrong servers. If your account is on the (formerly) US servers, you won't be able to log in to the Swiss servers, and vice versa. The (formerly) US servers are at neomailbox.com while the Swiss servers are at neomailbox.net. Make sure you're using the correct server name in your mail program's configuration.
Your account may have expired. You would have received several renewal reminders before we'd disable your account for non-payment. Contact us for more information if you think your account may have expired.
Your mail sending priveleges may have been disabled for exceeding the default limits on outgoing mail. See the next question.