Based on the error message it sounds like you may be getting a connection issue between your system and the server.
As data must travel between 15-30 (on average) servers (all owned by different companies) before it hits the server your domain is on, if anyone one of these is experiencing an issue, it can prevent you from connecting via outlook (may also affect access to webpages / webmail but not allways).
You will also want to insure that you have the proper ports open on your router if you are on a network.
Run the following command from a cmd prompt, at the time you are unable to connect:
If on pc:
tracert YOURDOMAINNAME.COM
If on mac:
traceroute -I YOURDOMAIN.COM
If you see any lines that say "time out" within the results, this is indicative of a connection issue and you may need to contact your ISP.
If the traceroute shows timeouts in the last 4 hops (usually) then you would want to contact LP support at
support@lunarpages.com or support.lunarpages.com