How to fix DNS resolving issues on Mountain Lion after waking from sleep?
I've had this exact same experience, though not every time. Sometimes it means sites that I have visited recently are unavailable but other sites I haven't visited in ages load just fine.
Usually flushing the DNS cache resolves it.
sudo killall -HUP mDNSResponder
Occasionally I get this as well. When it happens, I tell the system to flush the DNS:
# As root or sudo it
dscacheutil -flushcache
In the power settings, to avoid sleep/wake related issues, I've disabled the system's "put disk to sleep" option, as apparently, it can cause issues with SSD equiped boxes.