Interesting idea. I wonder how much height difference you would need so that gravity gives you enough energy to power the regenerator at the bottom? The actual energy would come from ... the gravity field of the Earth?
But second law of thermo dynamics applies. If this works at all it is because you are capturing a little more of the energy that was put in at the top and would otherwise be lost. You stil need to put in external energy to keep this system running.
If the process was 100% reversible, and friction free (probably a couple other loss factors I forgot about) it would be energy positive as the oxygen is making its way back up in the air is an external energy input. Of course in the real world both assumptions are wrong by more than enough that you can never get this to work.