yeah it could just be hibernating and needs the power button to start back up, or it could be a more serious issue.
Maybe it is suddenly getting too hot, and as a result shutting itself down before it is destroyed by heat.
Maybe it's something else. Do you have any new things attached to it? I once had a Maxtor 300GB External hard drive connected to mine, and when I deleted it's syncing software off the mac -- the mac would just shut down on me randomly.
I pinpointed the cause was the External HDD, it was dismounting itself from finder at random, and when it randomly cuts out like that, the computer crashed. I re-installed the software on the mac, and it worked find afterwards.
edit: the power button to turn it on, does it reboot completely? Or does it instantly bring you to the login screen which then brings you to the desktop?
Or does it do the chime, with the grey screen, load, bring up the login screen, and re-load the dock, programs & such?
The first one indicated it was hibernating, and returned to normal, the second one with the chime and a complete boot means it was actually powered off.