Recently I observed a very strange behavior of dhcpcd which I have't seen before: basically my ISP dropped the connectivity to most of the public Internet for a short time. During that time my Pi was only affected by means of not being able to reach it's DNS resolvers (those are public IPs which belong to the ISP). There wasn't any loss of physical connectivity so to speak, meaning no interface was down etc as the internal LAN was intact.
So after connectivity was restored the Pi could not resolve any FQDNs. I figured it must have flagged the DNS IPs as timed out after many unsuccessful attempts to resolve during the outage. I let it sit. Well 12 hours later the Pi was still unable to resolve so I had to restart dhcpcd and immediately DNS started working.
I'm running the following Pi and dhcpcd (which came with the OS, no additional software installed):