From what I understand, the increased sinking rate, happened for no special reason. Once water found its way to the top most of Titanic's structure, the water had unlimited access to the ship; where before the water would have to continue rising inside the hull to reach the top, now it could flood upwards, while also flood downwards.
The water inside the hull would be at level with the water inside the hull, therefore, until the hull is submerged, the hull still has some buoyancy. Once the water reaches over the structure, air is more rapidly displaced, and buoyancy is more rapidly lost.
To pull a Jim (with all do respect btw), you can try this at home with a shallow pan (or tupperware) in a sink or tube, full of water(at least a depth where pan can sink). Slowly fill pan with water, and the pan will sink lower, until the lip of the pan goes below the waterline, and then the pan sinks rapidly.
The break up did not have anything to do with the initial rapid flooding. In fact, the break up seems to have had the opposite effect on the stern section, as it righted itself, when otherwise it would have probably tipped over and sank with the rest of the hull. The break up was caused by the ship sinking to an angle the structure could not handle. This angle was achieved by the more rapid flooding. Where most ships tip over before such angle Titanic did not.