We report on a new measurement of the parity-violating asymmetry in quasielastic electron scattering from the deuteron at backward angles at Q(2)=0.038 (GeV/c)(2). This quantity provides a determination of the neutral weak axial vector form factor of the nucleon, which can potentially receive large electroweak corrections. The measured asymmetry A=-3.51+/-0.57 (stat)+/-0.58 (syst) ppm is consistent with theoretical predictions. We also report on updated results of the previous experiment at Q(2)=0.091 (GeV/c)(2), which are also consistent with theoretical predictions.