As of about 3pm PDT today, about 50% of the requests made to my webserver via the domain name have failed from various locations worldwide (as reported by my monitoring service Pingdom). The error that Pingdom reports in their logs is "No route to host". When I try to access the website myself, I am able to connect only about half the time. However when I try accessing it by its IP number, the site immediately comes up. GoDaddy provides my DNS hosting services, and I have not made any changes to the A record in months. The A record is pointing to the correct IP number. I contacted GoDaddy, but they insist it is not a DNS issue and pointed me to the website http://www.whatsmydns.net/#A/. This tool showed that my domain name quickly resolves to the correct IP from all locations. But my hosting company, which so far has been very competent in resolving issues quickly, insists it's a DNS issue. They are not experiencing any issues, and the datacenter where my server is located (it's a hostway DC) says that they are not experiencing any issues at the time. I have not touched the Apache config files recently at all.
Where else might the problem be?