This longitudinal study explores persistence in research productivity over time. We examine the trajectories of the academic careers of 2,326 current full professors in 14 STEMM disciplines, studying their lifetime biographical histories and publication histories. Every full professor is compared in terms of productivity classes (top, middle, bottom) with their peers at earlier career stages. We used prestige-normalized productivity in which more weight is given to articles in high-impact than in low-impact journals, recognizing the highly stratified nature of academic science. Our results show that membership in top productivity classes is to a large extent determined by being in these classes earlier. Half of the current top productive full professors belonged to top productivity classes throughout their academic careers. Half of the top productive assistant professors continued as top productive associate professors, and half of the top productive associate professors continued as top productive full professors (52.6% and 50.8%). Top-to-bottom and bottom-to-top transitions in productivity classes occurred marginally. The combination of biographical and demographic data with raw Scopus publication data from the past 50 years (N=1 million) made it possible to assign all full professors retrospective to different productivity, promotion age, and promotion speed classes. In logistic regression models, two powerful predictors of belonging to the top productivity class for full professors were being highly productive as assistant professors and as associate professors (increasing the odds by 180% and 360%). Neither gender nor age (biological or academic) emerged as statistically significant. Hiring both low-productivity and high-productivity scientists may have long-standing consequences for institutions and the national science system: after entering the system and achieving job stability, scientists in Poland (where attrition is low) usually remain in the system for years, if not decades.