The method of Invisible Invariants was developed in order to verify safety properties of parametrized systems in a fully automatic manner. In this paper, we apply the method of invisible invariant to "bounded response" properties, i.e., liveness properties of the type p q that are bounded - once a p-state is reached, it takes a bounded number of rounds (where a round is a sequence of steps in which each process has been given a chance to proceed) to reach a q-state - thus, they are essentially safety properties. With a "liveness monitor" that observes certain behavior of a system, establishing "bounded response" properties over the system is reduced to the verification of invariant properties. It is often the case that the inductive invariants for systems with "liveness monitors" contain assertions of a certain form that the original method of invisible invariant is not able to generate, nor to check inductiveness. To accommodate invariants of such forms, we extend the techniques used for invariant generation, as well as the small model theorem for validity check.