Mailbox Not Checking External POP3 Account

I have a third-party account that I am trying to check with my Verizon e-mail account. I have logged into Verizon’s webmail, gone to “My Settings,” and added the POP3 e-mail account via the POP tab. I have provided the correct information, but it seems that Verizon is not checking the mailbox properly. I have tested both over a secure connection on port 995 and without the secure connection on port 110. It looks like Verizon is connecting to my mail server and logging in but then it closes the connection. The server has the following error message:

Socket [968] error during [STAT] command from host. Socket was disconnected - Error: (10054)

Do you have any ideas as to what the problem is? It would be great if I could consolidate my e-mail into one e-mail inbox.  

Thank you for your help.