We predict that the maximal, steady-state ion capacity Ns(λ) of radio-frequency (rf) traps, loaded at a rate of λ particles per rf cycle, shows universal, nonlinear, nonmonotonic behavior as a function of loading rate λ. The shape of Ns(λ), characterized by four dynamical regimes, is universal, i.e., it is predicted to manifest itself in all types of rf traps independent of the details of their construction and independent of particle species loaded. For λ ≪ 1 (Region I), as expected, Ns(λ) increases monotonically with λ. However, contrary to intuition, at intermediate λ ∼ 1 (Region II), Ns(λ) reaches a maximum, followed by a local minimum of Ns(λ) (Region III). For λ ≫ 1 (Region IV), Ns(λ) again rises monotonically. In Region IV numerical simulations, analytical calculations, and experiments show Ns(λ) ∼ λ 2/3 . We confirm our predictions both experimentally with MOT-loaded Na + ions stored in a hybrid ion-neutral trap and numerically with the help of detailed ab-initio molecular-dynamics simulations.