In a former paper, we defined a new semantics for timed automata, the Almost ASAP semantics, which is parameterized by Delta to cope with the reaction delay of the controller. We showed that this semantics is implementable provided there exists a strictly positive value for the parameter Delta for which the strategy is correct. In this paper, we define the implementability problem to be the question of existence of such a Delta. We show that this question is closely related to a notion of robustness for timed automata defined in [Pur98] and prove that the implementability problem is decidable.