As Katella showed, the problem is happening right after flagtel.com server. When connection was properly working, there were 3 flagtel servers on the route, so the second one seems to be broken.

Considering flagtel.com seems to be on the route only for Frontier FiOS, I hoped Frontier could give me some clue, but tech with whom I chatted either did not know how to figure it out or did not care.

Frontier says they cannot help because the problem is happening after packet leaves Frontier network, so we probably should contact flagtel.com directly, but the problem is, I'm not even sure which company it is, much less how to contact them.

I created a support ticket with SE just in case they have better idea, but no replies yet.