Here's my fix, one that stuck after I figured out what was going on. It's not just a Comcast thing, or an Apple AE/TC thing - I've got offices on a few different ISPs, plus Comcast residential and business accounts. Once I figured it out - using Console and Little Snitch - it was a stupid simple fix, especially when I found that all of my CL fiber or all of my Comcast cable connections were pretty much crapping out at about the same time. If you followed the instructions, like I did, it just works - until it doesn't...
Comcast pings their modems for lots of reasons, with firmware updates being the least likely reason - lease renewals are more likely. What happens at these lease renewals is a soft reboot of the modem - which includes temporarily reactivating the DHCP server built into the router and temporarily reactivating NAT, and you know the rest. Double NAT, and a need for a double expresso or a double Irish Whiskey...
Almost all of my cable modems ship with a default 192.168.xxx.xxx address (the one I'm on now - a Netgear CM500 uses 192.168.100.1 but the Motorola SB6141 I used before that uses 192.168.1.1 and IMO there's issues with this "older" but still common address, read on). Following the installation instructions for your AE/TC relative to any of Comcast's modems (all of mine are purchased from a reseller, even for my BCI accounts - this does not matter here) generally yields a iPv4 DHCP Range of 192.168.1.2 to 192.168.1.200.
With my SB6141 and a couple of the BCI-issued modems were trying to temporarily assign the same DHCP Range of 192.168.1.2 to 192.168.1.200 during this lease renewal that the AE/TC is trying to assign to your network, and there's your Double NAT issue...
There's two fixes, on in software and the other in hardware. The hardware fix is simple - buy a modem that uses a different IP address, like the newer Arris SB6183 or CM500 - both use the same Broadcom chipset and 192.168.100.1 address.
Before I ponied up for a few new modems, the software fix is to change in Airport Utility from the iPv4 DHCP Range of 192.168.1.2 to 192.168.1.200 to one of the two different options - after switching (in the Utility's Network>Network Options... settings) to a Range of 10.0.1.2 to 10.0.1.200 I have had zero issues between my modems and AE/TC devices and other routers, and zero down time. Once a week, my modems phone home, eventually sync and get a new lease, and I never notice a thing...
Get your AE/TC/router DHCP Range assignment as far away as you can from the router's default IP range - or just on a different range of numbers. I hope this helps. If it does, mail a couple of fingers of Irish Whiskey to me - you won't need it!