Things you might ask/check:
Can it resolve at all when it has a problem?
What does nslookup tell you?
Does it have problems resolving any other sites?
Any events of note? Network issues?
Can you telnet to port 53 of the name server when there are problems?
Can you telnet to port 80 of the site name and/or the ip address of the site?
Are you using a proxy?
Are you using multiple DNS servers?
How many A records are there for this site?
Can this host access all of them?
Is it worth you or your companies time fixing this? Rebuild time perhaps?