I would think that the fall of a big organization would come from a few different things. Primarily it would come from bad leadership or lack of structure and/or purpose. Although you would think that if the organization was a big one it would have had some kind of direction at some point. Obviously another thing that could end an organization would be its absorption into a larger organization either willingly or by force. People might get bored and leave but for the most part I think that if you have good structure and a purpose you should be able to find people to join.
I am certainly interested to see how all of this plays out in DU because from what I read this game will likely have the most sophisticated form of player run politics and economy, which will of course dictate the way that organizations are run. For instance I am thinking you will see a lot of small organizations like mining companies, security forces, and even banking and trade guilds. These smaller organizations will likely be integrated into larger organizations that are in charge of the infrastructure and politics of territories and eventually perhaps entire planets or even systems.
It is the whole idea of the game that the players are what define the history of this new chapter of humanity so it is almost certain that as the game progresses you will see the rise and fall of empires and a perpetual struggle for power over planets and systems.
Sounds fun to me!