Internet drops only during Skype calls

My household bought a brand new router and modem a week ago and the equipment itself is totally fine. I have greatly improved internet speeds with it through Cox Communications and no compatibility issues between the router/modem or any computers using it. However, once I start a videocall or regular voicecall in Skype the internet totally drops on all systems, wireless or wired. There is a desktop connected to the router via ethernet cord directly and then two laptops in the household that, of course, connect through wifi. The coax cable is also brand new as we had tech support from Cox come out to check on everything because of the dropping issues just incase it was an in-home problem; They discovered our cable was sending noise to the box outside and put a new one in its place. After this I tried a skype videocall and once again the dropping persisted. It is intermittent - sometimes the call lasts 90 minutes other times just 2. Below I have included the three computer types, the router model, and the modem model. I stress that the problem only happens when Skype is involved. I do have a BitTorrent program which I have changed settings on after reading that it can cause interference with Skype, and use Second Life on a daily basis but the internet does not cut out when on the 3D chat/game - it is strictly when Skype is in a call. I have also updated to the most recent non-beta firmware for the router and the issue happened with or without the update.

Lastly I want to note that I have done extensive googling on settings to change and have come to no conclusion. It continues even if (under Skype connectivity settings) uPNP is on/off, if I turn on/off Skype wifi, and regardless if Use port 80 and 443 is checked or unchecked. And the cutting effects all computers not just the one using Skype (my laptop). It basically causes the router to restart itself (I have included the message the router login page has during an internet drop and also part of what the log reads from the router page after it comes back on). I will be checking for replies regularly so if anymore information is needed I will gladly provide it.

Desktop, 2 laptops: All Windows 7 64-bit
Router: Asus RT-N66U
Modem: Motorola/Arris SURFboard SB6141

During outage:
Settings have been updated. Web page will now refresh.
Changes have been made to the IP address or port number. You will now be disconnected from RT-N66U.
To access the settings of RT-N66U, reconnect to the wireless network and use the updated IP address and port number.

Router System Log:
Oct 17 00:23:54 rc_service: ntp 467:notify_rc restart_upnp
Oct 17 00:23:54 rc_service: ntp 467:notify_rc restart_diskmon
Oct 17 00:23:54 rc_service: waitting "restart_upnp" via ntp ...
Oct 17 00:23:54 miniupnpd[468]: received signal 15, good-bye
Oct 17 00:23:54 disk monitor: be idle
Oct 17 00:23:54 miniupnpd[476]: HTTP listening on port 37312
Oct 17 00:23:54 miniupnpd[476]: Listening for NAT-PMP traffic on port 5351
Oct 17 00:23:55 dhcp client: bound xx.xxx.xx.xxx via xx.xxx.xx.x during 86400 seconds.
Oct 17 00:24:34 crond[371]: time disparity of 2520444 minutes detected