I have been having this issue of losing my internet connection after waking my iMac. Searching around I found this issue discussed elsewhere, and the issue seems to be cause by Apple using two different methods for resolving domain names in Snow Leopard: (1) the UNIX way and (2) Apple's own lets-be-really-smart-about-it-and-out-smart-ourselves-way. Apple's headline software (Safari, Mail, iTunes, etc.) uses this new "smarter" way, while non-Apple software and including the Network Diagnostics use the UNIX way (which is why Network Diagnostics tells you nothing is wrong with your internet connection, while Safari says you're not connected). The issue is caused by Apple's way getting out of sync with the UNIX way. The fix I've seen in these other discussions is to shutdown and restart this "smarter" service using the following terminal commands:



sudo launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
sudo launchctl load /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist



This "fix" (until it happens again on a wake from sleep) has kept me from having to reboot my iMac every other day.