We have seen this problem rarely with some of our customers. They CAN browse their site thru their direct IP like http://xxx.xxx.xxx.xxx/, however they CAN NOT browse their site thru their domain name like http://mydoamin.com. Interestingly, this ONLY happens with some visitors from a specific ISP only. The rest of the world CAN browse the domain perfectly fine.
This issue is NOT a server or domain specific problem at our side. This problem actually happens due to the stale/outdated DNS cache at your Internet Service Provider's (ISP) DNS server. But, unfortunately we don't have any control over any ISPs, so there's nothing we can do about it. However, you can still resolve this issue as shown below.
Permanent Solution: Please call your ISP and tell them to refresh their DNS cache. Remember to tell them that you can correctly browse your domain thru another ISP or thru a Public Proxy like https://www.megaproxy.com/freesurf/ . Once your ISP refreshes their DNS cache, this issue will automatically get resolved permanently.
Temporary Solution: There's an workaround to resolve this situation temporarily. It requires the visitor (who is trying to browse your domain, but can't get it) to map the domain name with its IP on his OWN computer. On Windows machine, this can be done by adding an entry into the "hosts" file located under folder "C:\WINDOWS\system32\drivers\etc". To know the IP of the domain, simply use the link http://whois.domaintools.com/yahoo.com (use your domain instead of yahoo.com).