How does taking the full course of antibiotics prevent antibiotic resistant bacteria establishing in patients? We address this question by testing the possibility that horizontal/lateral gene transfer (HGT) is critical for the accumulation of the antibiotic-resistance phenotype while bacteria are under antibiotic stress. Most antibiotics prevent bacterial reproduction, some by preventing de novo gene expression. Nevertheless, in some cases and at some concentrations, the effects of most antibiotics on gene expression may not be irreversible. If the stress is removed before the bacteria are cleared from the patients by normal turnover, gene expression restarts, converting the residual population to phenotypic resistance. Using mathematical models we investigate how static recipients of resistance genes carried by plasmids accumulate resistance genes, and how specifically an environment cycling between presence and absence of the antibiotic uniquely favors the evolution of horizontally mobile resistance genes. We found that the presence of static recipients can substantially increase the persistence of the plasmid and that this effect is most pronounced when the cost of carriage of the plasmid decreases the cell's growth rate by as much as a half or more. In addition, plasmid persistence can be enhanced even when conjugation rates are as low as half the rate required for the plasmid to persist as a parasite on its own.