Why isnt my xbox 360 saving game progress? my son has beeen playing lego indiana jones and kung fu panda?

ok this might be a dumb question but it the 360 isnt saving my sons progress on kung fu panda and lego indiana jones. even when the screen says saving after a level.|||Does the xbox have a HDD or a memory stick?|||is your hard drive (HDD) on the side of your xbox?