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Windows 10 interrupting local connections when NCSI probe fails

When I lose internet connectivity at home, and the Windows 10 NCSI probe fails, local connections are being interrupted as well. It’s not DHCP-related, as all machines involved on the LAN have static IP addresses, and I don’t recall having this problem with earlier versions of Windows.

Short of disabling NCSI or defeating it using my router and a web server on the LAN, is there any way to keep it from doing that? I like having the indicator on the screen, but the apparent assumption that no internet means no network at all is really annoying.