1. TO REPRODUCE - stop mysql:
If mysql is not running then on a JSON rpc request web server returns a HTML with error that mysql server is not available, the HTML is not visible but actually it's interpreted as true and the red message is not displayed. And in such a case httpd doesn't perform the check of trappers port at all.
The same happens if frontend switched to maintenance mode, just returned HTML is different.

2. TO REPRODUCE - stop httpd:
Another case is if httpd is not running - the message is not displayed too because connection was refused/rejected/timeouted etc.

We discussed 1st case with Sasha a bit.
To improve it we probably should perform redirect to a frontend page which will bring the the HTML response visible in browser.

For 2nd case: probably would be better, if possible, to display the red error message without page reloading, but with a bit different text, like:
Could not connect to frontend web server to check status of running zabbix server.