There is nothing in the mammalian body plan which forbids the evolution of a unidirectional respiratory system. It is perfectly possible to imagine a mammal with such a respiratory system. But why on Earth would it evolve?
The normal expected evolutionary response to lower oxygen levels would be larger and more efficient lungs, not the complicated mechanism birds developed to compensate for their small rigid lungs.
Thing is, mammals are not worse than birds at extracting oxygen from air. Yes, birds use their complicated mechanism for unidirectional breathing, but on the other hand mammals have much larger lungs, with much larger gas exchange surface.
For a detailed comparison between the respiratory systems of bats and of birds, see J. N. Maina's "What it takes to fly: the structural and functional respiratory refinements in birds and bats", in The Journal of Experimental Biology 203, 3045–3064 (2000). Money quote:
Bats improved a fundamentally mammalian lung to procure the large amounts of oxygen needed for flight. The lung/air sac system of birds is not therefore a prescriptive morphology for flight: the essence of its design can be found in the evolution of the reptilian lung, the immediate progenitor
stock from which birds arose. The attainment of flight is a classic paradigm of the remarkable adaptability inherent in organismal and organic biology for countering selective pressures by initiating elegant morphologies and physiologies.
Birds are theropod dinosaurs, more specifically maniraptoran coelurosaurs. They have inherited the basic design of their respiratory system from their dinosaurian ancestors. This design evolved in order to compensate for having a rigid rib cage; birds cannot inflate their lungs, so that by necessity the part of the respiratory system which inflates to inhale and deflates to exhale has to be placed beyond the lungs. On the other hand, we mammals have can inflate and deflate our lungs, and we have plenty of room in our chests for big lungs, so that we do not need the avian mechanism of respiration.