Well I cannot nslookup on webmail.name-services.com. It comes back as unknown. If I nslookup using their dns server it returns (see below)
~$ nslookup
> server dns1.name-services.com
Default server: dns1.name-services.com
Address: 98.124.192.1#53
> webmail.name-services.com
Server: dns1.name-services.com
Address: 98.124.192.1#53
Name: webmail.name-services.com
Address: 69.64.157.76
I cannot connect to that IP on port 110. Is your webserver on their network? Or is it hosted elsewhere? Are you using them for your internet connection?
They may be limiting or preventing connections to their mail server from outside their network. Or they may have dns issues.
Try using 69.64.157.76 for the server name and see what happens.