The ion-hose instability is considered to be a potential danger for long-pulse, high-current electron linear induction accelerators (LIAs). As is shown in this paper, it is also a concern for multipulse LIAs. This instability is a direct result of beam-electron ionization of residual background gas, and the growth rate is proportional to the ion density. In a typical accelerator vacuum, there is little ion density decay between beam pulses, and the instability will grow throughout the pulse train. We have simulated this effect, taking into account ion density decay due to recombination and channel expansion. These simulations were done for the new 2-kA, 20-MeV Scorpius multipulse LIA presently being developed. The simulations have shown that the magnetic focusing field designed for Scorpius will be strong enough to inhibit ion-hose instability if the background pressure is kept below a value that is readily attainable with the present designs of induction cells and other accelerator components.