I noticed with my running server that Dinnerbone's Minecraft Server Status Checker reports that "Unfortunately, we were unable to contact this server."

Curious, I downloaded the source for his tool and tried it myself – same result. Thinking it might be a configuration issue, I created a brand new server and tried that, but it was still unpingable. I then realized I was using an old-ish version of Spigot, so I rebuilt from source, but it still didn't work. I downloaded the vanilla MC server, started it up, and the tool was able to talk to it just fine. I tried the CraftBukkit jar that BuildTools creates, but that also did not respond.