Why would composites continually fall out after just being placed?

I believe success with bonded composite fillings is largely dependent on the knowledge and technique of the dentist. Draw your own conclusions, but maybe it's time to get another look from a doc who you know is totally up on all the latest stuff. Unless something really weird's going on with your teeth, they should not be coming out like that.

What area of the tooth was the bonding placed? Some surfaces of the tooth are very hard for bondings to stay put. Usually dentists will inform their patients of this ahead of time. Also is it a large bonding or small?

There are a number of reasons. If the tooth getting worked on gets wet before the filling material is cured ( an ultraviolet light is used to harden the material) it will interfere with the bond between the filling and the tooth. If the filling is in the front and you are biting directly with the filling, that will make them fall out a lot of the time. As was already mentioned, a lot also falls on the knowledge of the person placing the filling.