When memories are reactivated during sleep, they are potentially transformed and strengthened. However, disturbed sleep may make this process ineffective. In a prior study, memories formed shortly before sleep were weakened by auditory stimulation when that stimulation provoked memory reactivation while also disrupting sleep -- a procedure known as targeted memory reactivation with sleep disruption (TMR-SD). Here we used TMR-SD to test whether memory weakening occurs for less-fragile memories. Participants first learned locations of 74 objects on a monitor. One week later, TMR-SD auditory cues linked with 50% of the previously learned object locations were presented during sleep. Even though the cues disturbed sleep, memories were not weakened when reactivated in this way, compared to when not reactivated. Whereas memory storage is vulnerable to disruption shortly after learning, this new evidence supports the notion that memory storage gradually gains resistance to the harm caused by reactivation combined with sleep disruption.