EDIT: I see from your earlier posts that you are using an iMac G5. I don't think the disk's automatically eject though. When do they eject? After a game, watching a DVD...?
If I install something and it asks for a new disc it pops out the disc that's already in, not a big deal, just annoying if I leave the room and come back finding a disc on the ground all scratched up. Probably just have to be patient with installations for now on or rig something up for discs to fall into.
The CD should stop mid-way, not completely fall out of its holding... unless you've set it up on a completely vertical angle. It might be a hardware issue - I'd have it checked if it's actually doing that.