Mavericks Wifi drops when display sleeps

I'm having a really strange issue with my iMac on Mavericks. I often stream movies from the iMac to my Apple TV, and after upgrading to Mavericks, the movies stop after three minutes. It took me a while, but I think I've tracked it down to my Energy Saver settings. I've got it set for Computer Sleep never, not putting hard disks to sleep when possible, and the Display sleep at 3 minutes. I know it sounds bizarre, but I can't figure anything else out. I have to walk over to the iMac, wake the display back up, and my Airport Utility shows that it can't find my router. I turn WiFi off and back on, and everything works perfectly after that, including Airport Utility showing everything connected. Until the display goes back to sleep again, at which point I have to repeat the steps again. Is anyone else having this issue? Any ideas on how to fix it?