Until that time when you flush the cache on Solaris[1] and remove the entries for its own interfaces. Then it stops responding to ARP requests for itself. Now you have an even more fun issue to troubleshoot!
1. something silly like: "arp -a | awk '{print $2}' | xargs -n 1 arp -d". It's been a while and I don't think I was the original culprit.
And how do you fix that? I'm no Solaris guru obviously, but this looks like a chicken-and-egg problem. How do you actually go about fixing this? It's sounds very... Kafkesque
Actually if you think about it, you can reach the server even if it's not replying to ARPs as long as it's initiating connections to other devices on the same network. Say A is the server in question (not responding to ARPs) and it initiates a connection to B. In this case, B will learn A's MAC, and so B will be able to reach A until A's entry times out of B's MAC table. The router for that network also has A's MAC, but you may not have access to the network gear.
The intermittent connectivity to server A is what makes this problem so fun to diagnose. :-)
1. something silly like: "arp -a | awk '{print $2}' | xargs -n 1 arp -d". It's been a while and I don't think I was the original culprit.