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A variable specific-impulse magnetoplasma rocket (VASIMR) is a potential means of powering future deep space missions. The engine uses radiofrequency (RF) energy to first ionize argon with a helicon antenna and to subsequently heat the resulting plasma through ion cyclotron heating (ICH) which then creates thrust in a magnetic nozzle. Our previous studies have modeled the increased specific impulse and thrust generated in a collisionless plasma. This work includes ion-neutral collisions in the simulation, which reduces the number of ions in the plasma stream and thus reduces thrust. This study analyzes the loss of thruster efficiency caused by such collisions in the nozzle region of the VASIMR. The plasma is considered weakly ionized, and other plasma effects, such as ion-ion and ion-electron collisions, are ignored. MonteCarlo methods are used to determine ion losses from a stream of individual argon ions as they move along the engine. Neutral densities are inferred from stipulated mass flow rates and ionization fractions. These are functions of the initial ionization process involving a helicon antenna, whose properties are inferred from this study, but not directly dealt with. Ion temperatures, and hence velocities, are determined as products of the ICH process. Efficiency of the engine varies widely with initial mass flow rates and the subsequent neutral backgrounds these produce, but in this simple study, collisional losses are large, for even moderate neutral backgrounds. An effective VASIMR thus requires an extremely efficient initial ionization mechanism.