There are a few reasons why this might occur.
If you are trying to use the wrong port, you may see a "Connection to smtp.pobox.com denied" error. You should connect to
smtp.pobox.com: port 587
Some email programs try to automatically set up ports for you, and may have pre-filled an incorrect port number.
If your password isn't being sent, you will get a "Relay Access Denied" error. If it's from Pobox.com, then most likely your SMTP settings are not correct. Get instructions for your email application.
Try resetting your password, and make sure that you are using one of your current Pobox addresses to log in.
If you have recently sent a high volume of mail, your access to the SMTP server may also have been deactivated. If this happens, we will send you an email to tell you your access has been removed. Please contact customer service if you are not approved to use the SMTP server and let us know what happened.
If you know your settings are correct, please check the email address in your messages' From: header. The Pobox SMTP servers will not accept outgoing mail whose From: address is a domain which has a DMARC policy of "reject". We recommend setting your From: address to one of the aliases on your account.