There could be a couple of reasons for this:
Make sure you are using the correct ports and settings. For POP3, you should be using port 995 or port 110 with SSL enabled, and for IMAP port 993 with SSL enabled. For POP3 without SSL encryption, you can use port 112.
You could be trying to log in to the wrong servers. If your account was originally on the 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 or been disabled. If you can't send mail or log in to the Control Panel either, it's likely that your account has been disabled. If this is the case, contact support for more details.
If you're able to send mail and access the Control Panel, but unable to retrieve your mail, contact support and we'll look into it asap.