Hello everyone and thank you so much for your suggestions,
with the command “cmk -vv hostname” from the cli we receive a correct answer and no errors, the services that went in stale were not only “Check_mk” as in the screenshot but also others, within the file nagios.log we did not find any particular error.
With the command “cmk --debug -vvR” the problem seems to be solved, we are observing the behavior of the site that seems to be fine now, in any case we try to modify also the parameter num_client_threads in. /etc/nagios/nagios. d/mk-livestatus.cfg. and we will update you