Wifi Disconnects at least once a day

I have exactly the same problem with a NightHawk C7000.  It seems to be associated with periods of inactivity over 4 hours or so.

I think I have an accidental clue that might help someone smarter than I to figure it out.

I configured the old router (WNR3500) as a switch (DHCP off), and connected it to the C7000, with everything else connected to the WNR3500 (via switches).  This was to make it easier to swap out the replacement C7000 I was expecting, and not because I expected it to affect anything.  When the new C7000 arrived, I hooked it up and it was stable for 5 full days!  "Great," I thought, "it was just a faulty unit."  I noticed that the speed in this, the stable configuration, was slow, so I connected the switch with the devices that needed the speed directly to the C7000, and the speed increased to the expected level.  

The next day, and every day with that configuration, the instability recurred!!

Slow, stable configuration:  

ISP---C7000---WNR3500---3 switches---various devices

Fast, unstable configuration:  

ISP---C7000---WNR3500---2 switches---various devices

          \

           \---1 switch---various devices (mostly computers)

Previous, slow stable (for years) configuration:  

ISP---WNR3500---3 switches---various devices

            \

             \---DVR

My ISP is Comcast in the Baltimore City area.  All switches are NetGear ProSafe GigaBit, with different port counts.  I have 2 MOCA devices on the network, and POE filter.

I have an open ticket with NetGear.  They have made numerous suggestions, including setting MTU to 1400 and changing the DNS addresses, none of which helped.