Try this workaround - instead of tapping a key to wake your iMac, tap the power button on the rear case instead. That action causes a different "wake from sleep" event to occur. It may work for you.
This was a common problem that the last incremental OS X update was supposed to have solved. It did for most people, but for others it remains.
Current airport support on this site is for OS X 10.6, but I am already on OS X 10.8.3. Why Apple Support doesn't use updated system?
A good question for which I only have a cynical answer, and I'm trying to avoid that. This is the most recent article: Troubleshooting Wi-Fi issues in OS X Lion and Mac OS X v10.6
Its recommendations remain unchanged for Mountain Lion, but won't help resolve this problem anyway.