A nonmonotonic relaxation kinetic model [Ya. Ryabov et al., J. Phys. Chem. B 105, 1845 (2001)] is successfully applied to describe an intriguing slow down in the dielectric secondary gamma relaxation of polypropylene glycols (PPGs) with increasing temperature near the glass transition. The anomalous behavior is interpreted as a result of two simultaneous events: A thermal activation and a defect formation in the hydrogen bonded network formed by molecules of PPGs. This new insight into the molecular mechanism, which is responsible for the suggested sensitivity of the secondary process in PPGs to the glass transition phenomenon, is compared to our previous results obtained in terms of the minimal model for secondary relaxations.