Carrier grade NAT breaks a lot of things in subtle ways. E.g. our ISP does DS-Lite to encapsulate IPv4 in IPv6. For months, our internet connection would sometimes seem dead for a couple of minutes. The router was fine and had uplink.
At some point I figured out that it often happened after a device woke from sleep and that IPv6 continued to work fine. It turns out that Bittorrent Sync was culprit. When a device woke up, BTSync syncs any changes and opens a boatload of connections through different ports. Apparently, the ISP's carrier grade NAT has some QoS where it starts dropping connections if too many ports are opened at the same time.
We shut down BTSync on all devices and never encountered the problem again [1].
At the time Bittorrent Inc. and later Resilio did not really seem interested to add IPv6 support.
[1] Of course, another theory is that they intentionally throttle Bittorrent traffic, but that doesn't explain why no IPv4 connections could be made while IPv6 worked fine.