Horizontal gene transfer is common among viruses, while they also have highly compact genomes and tend to lose artificial genomic insertions rapidly. Understanding the stability of genomic insertions in viral genomes is therefore relevant for explaining and predicting their evolutionary patterns. Here, we revisit a large body of experimental research on a plant RNA virus, tobacco etch potyvirus (TEV), to identify the patterns underlying the stability of a range of homologous and heterologous insertions in the viral genome. We obtained a wide range of estimates for the recombination rate—the rate at which deletions removing the insertion occur—and these appeared to be independent of the type of insertion and its location. Of the factors we considered, recombination rate was the best predictor of insertion stability, although we could not identify the specific sequence characteristics that would help predict insertion instability. We also considered experimentally the possibility that functional insertions lead to higher mutational robustness through increased redundancy. However, our observations suggest that both functional and non-functional increases in genome size decreased the mutational robustness. Our results therefore demonstrate the importance of recombination rates for predicting the long-term stability and evolution of viral RNA genomes and suggest that there are unexpected drawbacks to increases in genome size for mutational robustness.