I run a network (I'm just a math teacher) at my school. We get random 10 or so minute periods (I'd guess three a day on average) where the Internet is not accessible from within the LAN. If I go to our sonicwall and do a ping test, I can resolve so it's definitely internal.
We have a Windows 2008 server that handles a small DHCP for cellphones, everything else is static. That is connected to a managed switch with about 15 Cat5e connections and three fiber branches that go to different parts of campus. At each of these parts there is another managed switch that branches out to the LAN.
Our cable Internet comes into one of these locations, goes through the supplied modem and into a Sonicwall. The Sonicwall, as I stated above, stays connected to the Internet when no one on the LAN can see it (plus our VOIP phones keep working and they don't go through the Sonicwall). The only wonky thing I can think of is that I have both the Sonicwall and Windows handing (the same) static IPs to our 16 Chromebook's mac addresses. If I don't do this, the Chromebooks look to the DHCP on Windows for an address. Quite infuriating, you cannot set static IPs at the Chromebooks. But the Internet drops even when those are off, so I discounted that.
I've run wireshark while pinging 184.108.40.206 and watched it go out and come back on, but I have no idea what I am looking for in all that data...