A theoretical basis for the regularity of supercontinent cycles is lacking. Here we show that periodic supercontinent cycles are unlikely if thermal instabilities originating at the core-mantle boundary are of sufficient strength. We couple multiple mobile continents with vigorous mantle convection in a spherical geometry. Regular supercontinent cycles lasting 400 ± 50 m.y. occur in idealized models with three continents and a mantle heated purely from within by radioactive decay. In a model incorporating six continents and strong mantle plumes, this regularity is broken and supercontinents form only sporadically. Our results suggest that periodic supercontinent cycles are unlikely to occur in realistic Earth models.