G5 gos without any warning, into sleep mode

I work on a 1 1/2 year old with OSX G5 one of the 20-inch flat-panel
I started experiencing a new problem where the computer suddenly, and without any warning, went into sleep mode. Pressing the space bar brought it back to life, but it soon went into sleep mode several more times -- each, like the first time, without being asked to do so.

It is Hardware or Software Problem ?

Could be a faulty power supply but you didn't give your model so can't check it out for you. I'm assuming, when you say 20-inch flat-panel it is an iMac.

Look here, determine which model you have and look at the recall programs still underway in the Exchanges & Extensions box in the right sidebar: if your serial number is in one of those lists, you get a free repair.