You have someone reset you, meaning they invite you into a squad, pass you the leadership and leave your squad. That will reset the instance.
^ You can instantly reset instances.
As for the final boss spawning, not 100% sure with Abbadon but you should need to have killed all bosses before hand (which you need to do to open the gates anyway, so I guess so). Only other reason she may not be spawning is if the instance is not reset, which you should already know when you enter the instance and get the timer or if the mobs are still dead and gates are open.
Never heard of Peach missing her shining moment, so if you are still stuck with it, try PMing a GM online to help you out.