If the problem is failure to resolve, then it pretty much has to be a problem with the DNS servers or configuration. It's possible, albeit unlikely, that Pingdom and the unnamed other service have broken caching resolvers. It's also possible, ableit unlikely, that theplanet has broken DNS servers.
It seems more likely that the DNS zone for your domain might be mis-configured, resulting in random failures. Lame delegation from the GTLD servers, for example, can result in intermittent failure. If you post the actual domain, we could tell you quite a bit more.
Some things to check:
dig ns example.com @f.root-servers.net
This will return a list of additional DNS servers that have been delegated to handle DNS for your TLD. Pick one and send the same query to it. For example:
dig ns example.com @f.gtld-servers.net
This should return a list of the servers that handle the DNS for your actual domain. Hopefully it will be
Next, move on to sending an
A request to each of the listed servers:
dig a example.com @ns1.theplanet.com
dig a example.com @ns2.theplanet.com
(Assuming that the GTLD server listed those servers.)
They should both return the same results, differing only in minor details like