A range of gene drive systems have been proposed that are predicted to increase their frequency and that of associated desirable genetic material even if they confer a fitness cost on individuals carrying them. Engineered underdominance (UD) is such a system and, in one version, is based on the introduction of two independently segregating transgenic constructs each carrying a lethal gene, a suppressor for the lethal at the other locus and a desirable genetic “cargo”. Under this system individuals carrying at least one copy of each construct (or no copies of either) are viable whilst those that possess just one of the transgenic constructs are non-viable. Previous theoretical work has explored various properties of these systems, concluding that they should persist indefinitely in absence of resistance or mutation. Here we study a population genetics model of UD gene drive that relaxes past assumptions by allowing for loss-of-function mutations in each introduced gene. We demonstrate that mutations are likely to cause UD systems to break down, eventually resulting in the elimination of introduced transgenes. We then go on to investigate the potential of releasing “free suppressor” carrying individuals as a new method for reversing UD gene drives and compare this to the release of wild-types; the only previously proposed reversal strategy for UD. This reveals that while free suppressor carrying individuals may represent an inexpensive reversal strategy due to extremely small release requirements, they are not able to return a fully wild-type population as rapidly as the release of wild-types.