Need help setting up Technicolor modem/router in Bridged mode

Hello,

I am having issues successfully setting up my home network with my Cox-provided Technicolor modem/router in Bridged mode, using my own router.  My network topology is as follows:

(Cox Technicolor modem - port 1) --> (router/firewall) --> (switch) --> (wireless access point) --> (WiFi laptop)

I've configured the port on my router/firewall statically, using the IP address/gateway/DNS address settings that the Technicolor modem/router uses when it operates as both modem and router.  I was not sure what subnet mask to use (was not visible in the Technicolor modem/router settings), so I used /24.  

I've setup my own router/firewall to use private 192.168.0.x/24 address space for DHCP to the LAN supported by the switch and wireless access point.  The WiFi laptop can successfully connect to my wireless network and obtain an IP address from the private address space configured on my router/firewall.  From the laptop I can ping the wireless access point, the switch, and the router/firewall successfully.  However, when I try continuous pings to the Technicolor modem (on 192.168.100.1), the pings will succeed and fail intermittently.  On a continuous ping test I'll see a handful of successful pings followed by some failures (destination unreachable), followed by another few successful pings, etc.  This cycle continuously repeats with varying numbers of successful & failed pings.  One constant I've noticed is that just before pings fail, the time is under 10ms, but upon recovering from a series of failures, the first successful ping takes considerably longer - 1000 to 3000+ milliseconds.  All subsequent successful pings take the usual <10ms time, until they fail and the cycle repeats itself.

Under this configuration I am not able to route out to the internet, and I'm left with no choice but to reset the Technicolor and put it back in modem/router mode. 

My question is:  am I setting up my own router correctly?  I tried configuring the router to obtain its IP/subnet/gateway/DNS configurations via DHCP but it does not seem to work.  When I configure everything statically (and while my ping test is yielding successful pings) I can see Cox's gateway in my routers ARP table.  This tells me that, at least briefly, my router is able to talk to Cox's gateway.  What am I doing wrong or missing?  

Sidenote:  I thought that maybe the ping errors were caused by the Technicolor modem not always responding correctly, but this does not seem to be the case.  I configured my laptop with a static IP in the 192.168.x.x address space and connected it directly to one of the ethernet ports on the Technicolor modem and all continuous pings come back successfully and under 10ms.