The platform for the replicator 2 was built with a simple locking mechanism to allow the plate to be removed and installed, for easier cleaning and maintenance. The clip at the back of the platform contains a small rubber grommet that acts as the device to apply pressure onto the plate in order to lock it against the pegs at the front of the platform. Over time with use this arrangement will begin to wear down and you will find that it does not spring back into position as quickly, this in turn would affect it's ability to apply enough pressure to the plate to keep it locked securely.
The design of this system is flawed in terms of longevity - the replicator 2 machines are now getting to an age where we have noticed that wearing over time and use has affected some aspects of the printer reducing its performance. If you are experiencing these symptoms, chances are the rubber grommet on your platform has lost its ability to quickly return to its natural shape and thus cannot apply enough pressure to the plate to keep it from moving.
Fortunately there are ways to help secure your plate to the platform. Tape: add some masking tape around the clip at the back of the platform to help it fit against the build plate more securely, push the clip forwards to lock the platform in place. The tape will add that extra layer needed to secure the build plate.
You can also add a filler between the clip and the bed. You can use tape or small rubber pads, there are also 3D models available on thingiverse that other users have created which prints out a small rubber spacer using flexible filament to help with this problem. The back clip was intended to spring back into position after being depressed, however after time the elasticity in the rubber grommet has reduced and so will affect its ability to apply enough pressure to the plate and lock it in place.