The stability of the ground-state of positron-polar molecule complexes [M,e(+)] has been explored for M = LiH,HF,H2O,BeO,LiF using variational and diffusion Monte Carlo techniques. Our simulations show that the ground-state of the complexes [LiH,e(+)](2,1)Sigma(+), [BeO,e(+)](2,1)Sigma(+), and [LiF,e(+)](2,1)Sigma(+) is stable against the dissociation either in the two fragments M and e(+) or in the ether two fragments M+ and Ps = [e(+),e(-)], while the ground-state of [H2O,e(+)](2,1)A(1), and of [HF,e(+)](2,1)Sigma(+) has an energy equal to the dissociation threshold, M and e(+). We also compare the predicted vertical positron affinity (PA) with high quality vertical electron affinity (EA) and discuss the relevant difference between the two values.