Increasing nonresponse rates is a pressing issue for many longitudinal panel studies. Respondents frequently either refuse participation in single survey waves (temporary dropout) or discontinue participation altogether (permanent dropout). Contemporary statistical methods that are used to elucidate predictors of survey nonresponse are typically limited to small variable sets and ignore complex interaction patterns. The innovative approach of Bayesian additive regression trees (BART) is an elegant way to overcome these limitations because it does not specify a parametric form for the relationship between the outcome and its predictors. We present a BART event history analysis that allows identifying predictors for different types of nonresponse to anticipate response rates for upcoming survey waves. We apply our novel method to data from the German National Educational Panel Study including N = 4,559 students in Grade 5 that observed nonresponse rates of up to 36% across five waves. A cross-validation and comparison with logistic regression models with least absolute shrinkage and selection operator penalization underline the advantages of the approach. Our results highlight the potential of Bayesian discrete-time event modeling for the long-term projection of panel stability across multiple survey waves. Finally, potential applications of this approach for operational use in survey management are outlined.