The primary cause of engines falling off in past crashes has been bad maintenance habits. Engines are taken off pretty regularly, if you take them off wrong it causes uneven wear on the attachment spot, which can cause localized failure which at flight speed spreads quickly (take a piece of paper tear it a little then hold it out your car window holding it by one side of the tear with the tear in front, same kind of thing). This is what took down the O'Hare DC10, because of how the engines were attached taking them off the right way was time consuming and many crews didn't do it the right way, the FAA issued a warning almost 18 months before the accident, didn't help.
It's technically feasable that once the tail flew off that caused the plane to go into a flat spin, this would apply lateral torque on the engine mountings which the really aren't designed to handle, this could have caused the engines to fall off. Then you've still got to explain the belly fire, which could (I suppose) have been caused by electrical surges when the FDR was yanked from the plane (those things connect to sensors all over the place, including the fuel tank). But that is an unprecedented level of collateral damage to be caused by losing the tail, all of it is technically possible but we've never seen any of that as snowball from that kind of initial damage before, much less ALL of it in one crash.
Which again pushes us in the direction of sabatoge, but man that's a lot to sabatoge. Given that each kind of damage we're talking has a minimum 50% chance of taking planes down (engine loss being the most survivable), if I were the bad guy and had that level of resources I'd do it to 4 different planes knowing at least 2 would crash, the passengers on the planes that didn't crash would be scared out of their minds, and no one would ever doubt that this was a terrorist act (no way 4 planes are having massive mechanical failure in the same day without help, just not happening). This would again result in the entire air fleet being grounded for a few days, once again doing massive damage to our economy.
If this was terrorist sabatoge then they're very powerful, but also very stupid. If this was mechanical failure sell all your stock in AA because having a plane this unsound coming 2 months after the whole fleet was grounded (good time for heavy maintenance) is unforgivable and I can't see that airline recovering from the confidence hit.