Coadaptation between bacterial hosts and plasmids frequently results in adaptive changes restricted exclusively to host genome leaving plasmids unchanged. To better understand this remarkable stability, we transformed naïve Escherichia coli cells with a plasmid carrying an antibiotic-resistance gene and forced them to adapt in a turbidostat environment. We then drew population samples at regular intervals and subjected them to duplex sequencing—a technique specifically designed for identification of low-frequency mutations. Variants at ten sites implicated in plasmid copy number control emerged almost immediately, tracked consistently across the experiment’s time points, and faded below detectable frequencies toward the end. This variation crash coincided with the emergence of mutations on the host chromosome. Mathematical modeling of trajectories for adaptive changes affecting plasmid copy number showed that such mutations cannot readily fix or even reach appreciable frequencies. We conclude that there is a strong selection against alterations of copy number even if it can provide a degree of growth advantage. This incentive is likely rooted in the complex interplay between mutated and wild-type plasmids constrained within a single cell and underscores the importance of understanding of intracellular plasmid variability.