Hi Felix,
Kappy is usually spot on but I respectfully beg to differ on this issue. Airport does not turn off when you put the iMac to sleep. And, it can take up to 10 seconds for the iMac to "wake up" and acknowledge the Airport network. It can, however, disconnect from Apple TV in sleep mode. For help with AppleTV go here:
http://discussions.apple.com/forum.jspa?forumID=1185
Also, the more apps you have open when you put the iMac to sleep, the longer it takes to wake up.
You could try deleting the Airport preference file: com.apple.airport.plist
It's here; /Users/YourName/Library/Preferences. Drag that file from the Preferences folder to the Trash, empty the Trash and reboot. Your iMac will create a new pref file for you.
Carolyn 🙂
Message was edited by: Carolyn Samit