School value-added models are increasingly used to measure schools' contributions to student success. At the same time, policymakers and researchers agree that schools should support students' socialemotional learning (SEL) as well as academic development. Yet, the evidence regarding whether schools can influence SEL and whether statistical growth models can appropriately measure this influence is limited. Recent work shows meaningful differences across schools in changes in SEL scores by grade (Loeb, Christian, Hough, Meyer, Rice, & West, 2019), but whether these differences represent the effects of schools is still unclear. The current paper builds upon this earlier work by examining the stability of the estimated school-by-grade effects on SEL across two years, using a large-scale SEL survey administered in California's CORE districts. We find that correlations among school effects in the same grades across different years are positive, but they are lower than those for math and English Language Arts (ELA). Schools in the top or the bottom of the school effect distribution are more persistent in their impacts across years than those in the middle of the distribution. Overall, the results provide evidence that these school effects measure real contributions to SEL. However, the low stability of effects from one year to the next draw into question whether including these school value-added measures of self-reported SEL in school performance frameworks and systems would be beneficial.