The analysis of persistence in innovation can improve the understanding of firm dynamics, anticipate the effects of the different policy actions, correct macroeconomic disequilibria, help in designing the correct policies to boost R&D and, consequently, generate prosperity. Persistence of innovation is empirically explored mostly using the case of innovation leaders or followers, which may not apply to countries with poorer performances in terms of innovation. Studying the case of a moderate innovator may shed some light into the different conditions of firms and their attitude towards persistence, as well as the adoption of different policy actions to observe this heterogeneity. Additionally, the effect of firm size and industry has not yet been fully explored by the literature on innovation persistence. The present paper analyses the persistence of innovation using a dynamic panel comprising 1099 firms operating in all economic sectors of a moderate innovator country, Portugal. Firms are observed in three waves of the Portuguese part of the Community Innovation Survey (CIS), from 2004 to 2010. Using the random effects probit model, the persistence hypothesis fails to be corroborated. Such result suggest that innovation policy programs do not have long-lasting effect on innovative behavior of firms and it is unlikely that incumbent past innovators be the drivers of creative accumulation and future innovation. There is, however, some evidence that new, smaller, innovators might lead the creative wave. In this vein, there might be a rational to encourage public policies targeting start-up firms and new market entrants when innovation is the main primary funding goal.