This paper deals with the problem of runtime enforcement (RE) in the context of reactive systems, which consists in modifying the outputs of a system minimally to ensure its correctness. In contrast to enforcers that can postpone events via buffering, enforcers for reactive systems must operate within the same reactive cycle, always yielding a (possibly modified) output. For safety properties, an enforcer makes sure to satisfy the property at each step. However, for general regular properties, one can only expect to satisfy the property eventually. There is then a risk that even under enforcement the satisfaction is indefinitely delayed, and the property is never actually satisfied. Forcing the satisfaction of regular or $\omega$-regular properties has been considered using bounded fairness and prompt eventuality. In this paper, we propose a new runtime enforcement framework for regular properties with prompt eventualities. Given an automaton specifying a property $\varphi$ and a bound $k$, the enforcer should never falsify $\varphi$ more than $k$ consecutive steps. We formally define this RE problem, characterize $k$-enforceability of automata, and exhibit the construction of the enforcer. Rather than fixing $k$, we also study whether $k$ can be computed to ensure $k$-enforceability or some maximal coverage of $\varphi$. We implement the $k$-prompt enforcement framework, and demonstrate its behaviour with varying $k$.