A plane that size can lose that altitude in less than a minute. If the engine falling off caused hydraulic problems, especially if the flaps retracted prematurely (possible but seems unlikely), then the plane would've had a very hard time staying in the air. Furthermore, they're finding pieces of the plane (such as the vertical stabilizer) well away from the primary impact site. That suggests the plane might've began breaking up before impact.

An aircraft accident is seldom caused by a single event like an engine failure. Accident investigators describe a "chain of events" that almost always leads to the crash. Pilots attend safety seminars at least once a year and we're trained on these chains. The goal is to break the chain and prevent a crash.

Consider the case of the Concorde crash last year. According to the official report, the plane hit a small piece of metal on the runway that had fallen off of an earlier plane. That metal caused the tire to rupture when the plane was going over 200 MPH. As a result, tire fragments (some weighing up to 5 KG) impacted the bottom of the plane's wing rupturing the fuel tanks. When the plane took off and the fire indicator lights came on, the flight engineer shut down one of the engines. The Concorde is a very low aspect ratio design, meaning induced drag is very high at low airspeeds. It appears the engineer also shut down a second engine which sealed the plane's fate. At that takeoff weight, the plane would've had to be flying faster than 400 MPH to climb on only two engines. It wasn't going nearly that fast. There are some reports that indicate the plane may've been overloaded as well with the center of gravity too far aft. If true, then the chain of events was pretty long. Had any one of these events been prevented from happening, the plane would not have crashed.

In today's crash, it's too soon to know the complete chain of events. Here's what's known right now:

The plane, an American Airlines Airbus A-300-600, took off from New York.

Shortly after takeoff, eye witnesses including airline pilots describe seeing smoke coming from the right engine.

It appears the right engine fell off of the plane at some point between the runway and the impact point. It further appears that other pieces may've fallen from the plane on the way.

It has been reported that the plane was in for maintenance just yesterday. It was also about an hour late for take off today, but no one seems to know if that was an ordinary delay or if it was due to mechanical problems.

As to the cause, I've posted below of at least 6 possibilities that I can think of off the top of my head. Terrorism and/or sabotage are possibilities but only that. There are reports of heavy bird activity in the area. There are also reports that the right engine had over 9700 flying hours on it and those engines are overhauled every 10,000 hours. Sabotage would be a deliberate act to cripple the plane. There is just as likely the possibility that some mechanic made a critical error that started the chain of events.

We may not know the true reason for months or even years. There was an airliner crash here in Colorado Springs back in 1991. The NTSB released their final report just this year, and even after all this time, they're not really certain what caused the plane to go down. The cause was described as a rudder malfunction but they never found out why that happened.