@_rb may I adress you here directly?
I think this is something for the Devs. You probably need to configure the Checkmk Agent Socket to allow more connections. See the link (paywall) below for reference. You basically need to configure the systemd unit file for the check-mk-agent.socket with a setting similar to this:
[Socket]
MaxConnectionsPerSource=20
I will be verifying this the next days and update here.
Update: I was just able to verify my suspicion. The value of MaxConnectionsPerSource is set to 3 by default. As we use a retry interval shorter than one minute (don’t ask) we probably trigger this limit and the socket stops responding until a reset. So from my point of view there are two possible solutions: Increase the value by default or make it configurable via Setup.
Link: systemd: <SomeService>.socket: Too many incoming connections (64) - Red Hat Customer Portal