I don't know anything about Ubuntu, what kernel version is it? I ask because I having the same problem with my server but it's Mandrake MNF, 2.4.18-8, and the server will suddenly stop responding, no pings and doesn't respond to keyboard or mouse, I need to push the power button to reset the computer. When it comes back up, it's fine, like nothing happened.
Also, what kind of server is it? specs? could it be a hardware problem like a bad memory card?