The kernel network stack is handling ICMP messages, which are those sent by the
If you do not get replies, besides network problems or filtering, and host based filtering/rate-limiting/black-holing/etc. it means the machine is probably overloaded by something, which can be transient, or the kernel crashed, which is rare but can happen (faulty hardware, etc.), not necessarily because of the ICMP traffic (but trying to overload it with such traffic can be a good test at the beginning of life of a server to see how it sustains things).
In the later case of kernel crash you should have ample information in the log files or on the console.
Also note that
ping is almost always the wrong tool to check if a service is online or not. For various reasons, but mostly because it does not mimic real application traffic, by definition.
For example if you need to check that a webserver is still live, you should instead do an HTTP query to it (TCP port 80 or 443), if you need to check a mailserver you do an SMTP query (TCP port 25), if a DNS server, an UDP and a TCP query to port 53, etc.