In this work, we have investigated and modeled an anomalous transient behaviour of the hydrogenated amorphous silicon (a-Si:H) thin film transistor (TFT) in a time scale (of the order of hundreds of seconds) where the threshold voltage shift is not prominent. Such a long term transient in the terminal characteristics can be critical in analog applications of the TFT, such as in pixel driver circuits of organic light emitting diode (OLED) displays. The reproducibility of the transient behaviour regardless of the presence or absence of any thermal annealing cycle suggests that the behaviour is not related to the metastable creation of defects in a-Si:H. The underlying mechanism that we believe is a configurational relaxation of Si dangling bond (D) defects after change in their charge states. Other possible effects including the properties of the source and drain contacts are carefully considered. Based on the defect relaxation mechanism, we have proposed a time dependent drain current model to describe the transient response of the TFT in the forward above threshold regime of operation. The parameters associated with the model are physically based and have strong dependence on the TFT geometry. The measurement data are in good agreement with the simulation results with a discrepancy of less than 5%, thus validating the model.