SARS-CoV-2 uses β1 programmed ribosomal frameshifting (β1 PRF) to control expression of key viral proteins. Because modulating β1 PRF can attenuate the virus, ligands binding to the RNA pseudoknot that stimulates β1 PRF may have therapeutic potential. Mutations in the pseudoknot have occurred during the pandemic, but how they affect β1 PRF efficiency and ligand activity is unknown. Studying a panel of six mutations in key regions of the pseudoknot, we found that most did not change β1 PRF levels, even when base-pairing was disrupted, but one led to a striking 3-fold decrease, suggesting SARS-CoV-2 may be less sensitive to β1 PRF modulation than expected. Examining the effects of a small-molecule β1 PRF inhibitor active against SARS-CoV-2, it had a similar effect on all mutants tested, regardless of basal β1 PRF efficiency, indicating that anti-frameshifting activity can be resistant to natural pseudoknot mutations. These results have important implications for therapeutic strategies targeting SARS-CoV-2 through modulation of β1 PRF.