Not a full on solution, but I've found that simply disabling and enabling the wireless network brings the chromecast back up. I prefer doing this since it doesn't take down my whole network.
I have the chromecast on a reserved IP in my DHCP pool, but that hasn't made a difference.
What I noticed just today when fooling with it, is that it looks like the chromecast keeps it's adhoc network alive even after it's initial setup. I'm only guessing, but I'm suspicious because after I restarted the wireless network, I noticed a "ghost" wireless network that was on another channel, follow over to the channel I've chosen from my network (AFAIK, none of my neighbors use this channel). I call it a ghost wireless network because it's open, but has no SSID. It probably has a real name, but this is the first time i've seen it.
Any ideas? Am I chasing a red herring here?