We have been investigating an electrochemical single-molecule counting experiment called nanopore resistive-pulse sensing. The sensor element is a conically shaped gold nanotube embedded in a thin polymeric membrane. We have been especially interested in counting protein molecules using these nanotube sensors. This is accomplished by placing the nanotube membrane between two electrolyte solutions, applying a transmembrane potential difference, and measuring the resulting ionic current flowing through the nanopore. In simplest terms, when a protein molecule enters and translocates the nanopore, it transiently blocks the ion current, resulting in a downward current pulse. We have found that the duration of such current-pulses are many orders of magnitude longer than the electrophoretic transport time of the protein through the nanotube detection zone. We develop here a simple model that accounts for this key, and previously explained, observation. This model assumes that the protein molecule engages in repeated adsorption/desorption events to/from the nanotube walls as it translocates through the detection zone. This model not only accounts for the long pulse duration but also for the triangular shape of the current pulse and the increase in the standard deviation of the pulse duration with increasing protein size. Furthermore, the results of our analyses are in general agreement with results obtained from other investigations of protein adsorption to surfaces. This includes the observations that smaller proteins stick more readily to the surface but remain adsorbed for shorter times than larger proteins. In addition, the sticking probabilities calculated from our data are in general agreement with results obtained from other methods.