Doesn't make much since if after the power is restored and all nodes are back up and running that you wouldn't be able to ping the server from a network node.
So how about the other direction can you ping a node from the server? Can the server ping itself and or the default gateway?
Just a shot in the dark but perhaps during the outage after some time of zero traffic the server OS is turning off the NIC, so.......
Check device manager, properties of the network adapter under the power tab and see what's checked.
And maybe just a simple ping out from the server might get things humming again, but you should probably uncheck the energy stuff for the server NIC.