Analytical treatment interruptions (ATIs) of antiretroviral therapy (ART) play a central role in evaluating the efficacy of HIV-1 treatment strategies targeting virus that persists despite ART. However, it remains unclear if ATIs alter the rebound-competent viral reservoir (RCVR), the virus population that persists during ART and from which viral recrudescence originates after ART discontinuation. To assess the impact of ATIs on the RCVR, we used a barcode sequence tagged SIV to track individual viral lineages through a series of ATIs in Rhesus macaques. We demonstrate that transient replication of individual rebounding lineages during an ATI can lead to their enrichment in the RCVR, increasing their probability of reactivating again after treatment discontinuation. These data establish that the RCVR can be altered by uncontrolled replication during ATI.