I am seeing the exact same problem as Ajax. I am using Cisco AnyConnect and some sites are periodically unresolvable. Frustrating. Just like Ajax, I can't ping the name, but I can do an nslookup to get the IP. Once I have the IP, I can ping the address with no problems. No problems at all hitting the internet while connected to VPN. We use a split tunnel.
One observation... Chrome does not seem to be as susceptible to the issue. Firefox and Safari will not load certain pages when the issue occurs. So, why does Chrome work. Does it somehow use the IP address? I am not sure how it resolves the address unless it is cached.