As I've moved things around I want to name them just for clarification.
Router A = Original, working, slightly faster router.
Router B = Newer, slightly slower router that drops WAN.
I haven't considered faulty hardware. The main reason I haven't is all the components are known working outside of this configuration. Both Intel NIC's were functioning properly in Router A. Router B's mobo and HDD were previously running FreeNAS with no noticeable problems.
As the constant loss of connection was driving me crazy, I moved Router A back in place. I changed Router B's LAN IP's to a different subnet (Not sure if that's the correct terminology, but I changed from a 192 address to a 10. address) and connected Router B's WAN to Router A's LAN. I also setup a test machine under Router B so I could see if the WAN connection gets dropped.
It's been running for a few hours now and not a single dropped WAN message from Router A or B. There were a few other strange messages in Router B. Ones that I don't see under Router A, but I accidentally cleared the log. Stupid me. It seems that I've narrowed it down to being a problem with Router B and my cable modem now working correctly? I'm using a SB6120 with Comcast. Assuming the strange messages show back up in Router B, I will definitely post them in the morning.
Thanks again for everyone's suggestions.
Edit: Logs Added
Jul 24 22:50:32 apinger: Starting Alarm Pinger, apinger(36545)
Jul 24 22:57:27 dhclient: RENEW
Jul 24 22:57:27 dhclient: Creating resolv.conf
Jul 24 23:57:27 dhclient: RENEW
Jul 24 23:57:27 dhclient: Creating resolv.conf
Jul 25 00:57:27 dhclient: RENEW
Jul 25 00:57:27 dhclient: Creating resolv.conf
Jul 25 01:57:27 dhclient: RENEW
Jul 25 01:57:27 dhclient: Creating resolv.conf
Jul 25 02:57:27 dhclient: RENEW
Jul 25 02:57:27 dhclient: Creating resolv.conf
Jul 25 03:57:27 dhclient: RENEW
Jul 25 03:57:27 dhclient: Creating resolv.conf
Jul 25 04:57:27 dhclient: RENEW
Jul 25 04:57:27 dhclient: Creating resolv.conf
Jul 25 05:57:27 dhclient: RENEW
Jul 25 05:57:27 dhclient: Creating resolv.conf