Perhaps you should do nothing except change the PHP script run time from unlimited to a sensible default. If there is a PHP script that is running for hours and days - and thereby hogging resources - then limiting the run time for such is script is all you need to do to solve the problem.
Your web server stops serving pages when it reaches a certain threshold of traffic. It is failing in the most graceful way possible.
The worse alternatives to this sort of failure is that the web server slows down to an unacceptable level of performance or the entire server hangs. In the present case all these bad things have been prevented from occuring due to a limit on the number of child processes. It would not be a good idea for you to increase the number of child processes / sub processes just to get rid of the error, because by doing so you might cause the web server to fail in a more ungraceful manner.
In summary, if you are unable to allocate more CPU and RAM to the server then you will have to identify the virtual server which is hogging resources and do something about it.
I’ve been running these setting with good results, halved the ram usage, this is in the template.
This only effect each virtual server only untill you disable and enable FPM, so you can do a staged change.