The study of protein adsorption at the single molecule level has recently revealed that the adsorption is reversible, but with a long-tailed residence time distribution which can be approximated with a sum of exponential functions putatively related to distinct adsorption sites. Here it is proposed that the shape of the residence time distribution results from an adsorption process with sequential and reversible steps that contribute to overall binding strength resembling "zippering". In this model, the survival function of the residence time distribution of single proteins varies from an exponential distribution for a single adsorption step to a power law distribution with exponent -1/2 for a large number of adsorption steps. The adsorption of fluorescently labeled fibrinogen to glass surfaces is experimentally studied with single molecule imaging. The experimental residence time distribution can be readily fit by the proposed model. This demonstrates that the observed long residence times can arise from stepwise adsorption rather than rare but strong binding sites and provides guidance for the control of protein adsorption to biomaterials.