Strange apache problem

I'm running apache 2.4 on FreeBSD 13.1-RELEASE.  Packages are up to date,
haven't installed kernel patches yet.

Starting about a week ago, sometimes the web server sort of ignores incoming
https connections.  The client connects, then nothing happens and the client
times out.  If I restart the web server, the client reports that the connection
is reset.  I see this from different clients on different machines connecting
from different networks, so it's not just one dodgy browser.

What is strange is if I retry the same web page from the same client a
few minutes later, it often works. The command line gnutls-cli usually
hangs, while LibreSSL 2.8.3 s_client works (that's the version of
openssl that comes with MacOS.)

I have tried rebuilding apache from source, no difference.  When I say it works
later from the same client, literally nothing has changed other than that I tried
later.  The server has been up for 165 days and this only started about a week ago.

Any suggestions keeping in mind that sometimes it works and sometimes
it doesn't with no pattern I can see? I'm baffled.

R's,
John