Messages video chat stops after 30 sec

Recently, I've found that after starting a Messages video chat, there is a significant chance that after about 30 sec the chat will drop unexpectedly. Messages reports no data has been received for the last 10 sec and offers to send a report to Apple. Sometimes my Airport Extreme appears to reboot kicking me off the internet, but other times it keeps going allowing me to reinitiate the video chat and continue for as long as we want to talk. The console shows no errors between the time the chat was established to the time the link is dropped. I do see errors after the event, but I'm not sure if they are related to the cause of the problem or just downstream errors. The problem started a few weeks ago around the time I replaced my old Airport Extreme with a new unit, but that may just be coincidence. Does the Airport Extreme generate a log that I can view?

Messages Connection Log:

2014-08-02 06:24:31 -0700: 0x61800019ee00: State change from Waiting to Connecting.

2014-08-02 06:24:33 -0700: 0x61800019ee00: State change from Connecting to Connected.

2014-08-02 06:25:18 -0700: 0x61800019ee00: State change from Connected to Ended.

2014-08-02 06:25:18 -0700: 0x61800019ee00: Error 1005 (No data has been received for the last 10 seconds.)

Console Log:

8/2/14 6:24:30.614 AM WindowServer[122]: _CGXRemoveWindowFromWindowMovementGroup: Window not in group

8/2/14 6:24:31.722 AM WindowServer[122]: _CGXRemoveWindowFromWindowMovementGroup: Window not in group

8/2/14 6:24:31.722 AM WindowServer[122]: _CGXRemoveWindowFromWindowMovementGroup: Window not in group

8/2/14 6:24:31.731 AM Messages[2158]: attribute = {

VCSupportARDAudioMux = 1;

shouldFindExternalIP = 1;

}

8/2/14 6:25:45.429 AM Messages[2158]: Saved diag report for Messages version 8.0 (4226) to /Users/xxx/Library/Containers/com.apple.iChat/Data/Library/Logs/DiagnosticRepor ts/Messages_2014-08-02-062545_xxx.diag

8/2/14 6:26:35.894 AM mDNSResponder[42]: SSLHandshake failed: -9806

Later on in Console Log:

8/2/14 6:29:10.765 AM mDNSResponder[42]: Double NAT (external NAT gateway address 192.168.100.10 is also a private RFC 1918 address)

8/2/14 6:29:12.775 AM mDNSResponder[42]: Double NAT (external NAT gateway address 192.168.100.10 is also a private RFC 1918 address)