What you are referring to is generally called the 'Late Bronze Age collapse' and occurred a little bit later, in the 13th and 12th century BCE.

The short answer is, we don't really know! It was a long time ago, after all.

The long answer is, it could be a lot of things, and likely a combination of several factors. The two main ones that are generally put forward today are environmental or migration. The first basically posits that a variety of environmental factors that differed from place to place contributed to the collapse. So, for example, you have earthquakes and eruptions on places like Crete, while in Mesopotamia you have droughts and soil degradation from over farming. There was also a 'Bond event' that could have resulted in lower crop yields across the basin (a similar event to the 'Little Ice Age' of the early modern period). So if all of these happen in a very short time, you could see a great straining on the resources of states, always running on a razors edge in terms of food supply, to deal with this. The other theory is the migration theory. In this theory, 'Sea People', who are mentioned in numerous primary sources, start moving into Greece, Anatolia, and Canaan, while simultaneously, nomadic tribes from the Caucuses and the Iranian Plateau move south as well.

One can see how these two are most likely linked though. If food supplies are dwindling and internal unrest is increased, you weaken your state against potential invasion. Environmental impacts also might have promoted the migration of these 'barbarian' peoples south in order to find food themselves. And of course, there were certainly unique factors in each particular polity that contributed to their collapse (or survival). I want to stress that last part though: survival. No where during this period of collapse was there a complete retrenchment of civilization. While the number and size of occupied sites fell dramatically, particularly in Greece, Asia Minor, and the Levant, this wasn't a complete destruction. In other places, despite a fracturing, civilization generally continued on (such as in Egypt or in the remnants of of the Hittite Empire (so called 'Neo-Hittite' states). And, those Sea Peoples and nomads that invaded certainly settled down and added to the cultural mix of the territories.

Drews puts forth a number of possibilities. Climate change, political crisis, earthquakes, invaders (or migration if you prefer), the invention of iron-working.... He himself prefers advancements in military technology. The armies of the bronze age seem to have been aristocratic guys in chariots. Chariots are expensive; it's hard to get large armies of them. They let someone move quickly while wearing heavy armor. Someone on the ground with a spear is not likely to be very effective against a chariot. Drews argues that this system of aristocratic chariot warfare made the political system legitimate, and when infantry began using armor that allowed them to move quickly and armor piercing weapons (I can't remember the particular sword Drews is interested in - Maybe someone out there can help?). Fast moving infantry could deal with chariots, and once infantry could deal with chariots, the legitimacy of the aristocracy collapsed.

It's been awhile since I read Drews; I might be forgetting something. And who knows if he's right?

Also, I think we're pretty sure the collapse was 1200-ish.