After switching to sensu-plugins/check-http + cmd_check_alert instead of alerta-urlmon, the stability of client site checks has increased significantly.
But it turned out that this plugin has an unsatisfactory dns timeout built into it.
The dns-timeout patch in the verification code made it possible to finally get rid of false positives and obtain stable monitoring of the site (availability, validity of the certificate, code, presence of text, etc.).
