Hi rhqq,
I’m also familiar with this behavior. I had also established the Internet connection via LTE - but via a USB modem.
I have noticed that in my case these connection breakdowns did not affect all devices at least. Weirdly, it mainly occurred on iOS/Mac devices. I had a guess (shot in the dark) that it was a firewall thing or related to knot-resolver. A SSH connection to the router was always possible.
Unfortunately I did not had the time to find a solution. I switched to another platform.