The effects of nonlinear resonances in a linear Paul trap have been investigated through systematic experiments and numerical simulations. The main causes of the nonlinearity that affects the stability of the ion motion are the use of circular (rather than hyperbolic) electrodes, their misalignments, and Coulomb interactions among the ions. A particle tracking code based on a two-dimensional model is employed to study the efficiency of plasma storage and to confirm the existence of nonlinear resonance stop bands. Experiments are performed with Ar+ plasmas that are eventually detected by a Faraday cup after a short storage. The obtained data are compared with numerical simulations in which the exact three-dimensional structure of the trap system has been incorporated. Several nonlinear stop bands have been experimentally identified inside the Mathieu stability region. It is demonstrated that the location of a resonance stop band moves due to the space-charge potential depending on the number of confined ions.