Win 8 Live Mail was also working fine for me until I upgrade to Win 8.1 this morning. Now it constantly give error message that it cannot find the email servers. I have 2 gmail (IMAP) account and one streamyx (POP3) account and all have similar errors. Please refer to error message and mail server set ups below. Please take note that I have no issue with all 3 mails when I use Windows Mail app. I have also repaired Win Essential 2012 successfully but problem did not go away.

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Unable to send or receive messages for the Gmail (hltaccntA) account. Header download for the 'Inbox' folder did not complete.
The host 'imap.gmail.com' could not be found. Please verify that you have entered the server name correctly.

Server Response: Your IMAP command could not be sent to the server, due to non-network errors.
This could, for example, indicate a lack of memory on your system.
Server: 'imap.gmail.com'
Windows Live Mail Error ID: 0x800CCC0E
Protocol: IMAP
Port: 993
Secure(SSL): Yes

Unable to send or receive messages for the Gmail (hltaccntB) account. Header download for the 'Inbox' folder did not complete.
The host 'imap.gmail.com' could not be found. Please verify that you have entered the server name correctly.

Server Response: Your IMAP command could not be sent to the server, due to non-network errors.
This could, for example, indicate a lack of memory on your system.
Server: 'imap.gmail.com'
Windows Live Mail Error ID: 0x800CCC0E
Protocol: IMAP
Port: 993
Secure(SSL): Yes

Unable to send or receive messages for the Streamyx (hlt*****8) account. The host 'pop.streamyx.com' could not be found.
Please verify that you have entered the server name correctly.

Server: 'pop.streamyx.com'
Windows Live Mail Error ID: 0x800CCC0D
Protocol: POP3
Port: 110
Secure(SSL): No
Socket Error: 11003

There was an error when attempting to connect to the Windows Live Calendar service.
If the error persists, check to see if there's an upgrade of Windows Live Mail available or contact a service representative.

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Mail server settings :

IMAP setting for both hltaccntA and hltaccntB gmail account as below:
Incoming mail server : imap.gmail.com
Outgoing mail server : smtp.gmail.com
Log on using clear text authentication

Outgoing Mail Server requires authentication and uses same setting as incoming email server
Outgoing SMTP using SSL and Port 465
Incoming IMAP using SSL and Port 993

POP3 setting for Streamyx account as below :
Incoming mail server : pop.streamyx.com
Outgoing mail server : smtp.streamyx.com
Log on using clear text authentication

Outgoing Mail Server requires authentication and uses same setting as incoming email server
Outgoing SMTP using Port 25 and no SSL
Incoming IMAP using Port 110 and no SSL