Thank you for your message.
Can you please provide us the URL from one of the websites so we can have a look on our side. When the website is not available, can you please check the HTTP response status code returned by the web server.
If the code belongs to the range 2xx, then the HTTP is working as expected as indicated in this kb article: https://kb.paessler.com/en/topic/65731-which-http-status-code-leads-to-which-http-sensor-status
Depending on the error page you get, you could use a custom script (examples available here) with an EXE/Script or EXE/Script Advanced sensor, which will take the error page into account independently of the response code.
If you have questions, let us know.