The Husimi distribution function is used to study the phase-space localization of Rydberg wave packets produced in a quasi one-dimensional hydrogen atom by the impact of half-cycle pulses (HCPs). The wave packet in a single-kicked atom exhibits transient phase-space localization. A weak second time-delayed HCP is found to extend the time of localization provided it is applied when the wave packet is near the inner turning point of the classical electron trajectory and momentum-transfer vectors of the first and the second kicks have the same sign. Alternatively, application of a similar second HCP increases the atomic ionization probability if the momentum-transfer vectors of the two kicks have opposite directions.