Organic field-effect transistors exhibit operational instabilities when a gate bias is applied. For a constant gate bias the threshold voltage shifts towards the applied gate bias voltage, an effect known as the bias-stress effect. We have performed a detailed experimental and theoretical study of operational instabilities in p-type transistors with silicon-dioxide gate dielectric. We propose a mechanism in which holes in the semiconductor are converted into protons in the presence of water and a reversible migration of these protons into the gate dielectric to explain the instabilities in organic transistors. We show how redistribution of charge between holes in the semiconductor and protons in the gate dielectric can consistently explain the experimental observations. Furthermore, we explain in detail the recovery of a pres-stressed transistor on applying zero gate bias. We show that recovery dynamics depends strongly on the extent of stressing. Our mechanism is consistent with the known aspects of bias-stress effect like acceleration due to humidity, constant activation energy and reversibility.