Like many chronic diseases, human immunodeficiency virus (HIV) is managed over time at regular clinic visits. At each visit, patient features are assessed, treatments are prescribed, and a subsequent visit is scheduled. There is a need for data-driven methods for both predicting retention and recommending scheduling decisions that optimize retention. Prediction models can be useful for estimating retention rates across a range of scheduling options. However, training such models with electronic health records (EHR) involves several complexities. First, formal causal inference methods are needed to adjust for observed confounding when estimating retention rates under counterfactual scheduling decisions. Second, competing events such as death preclude retention, while censoring events render retention missing. Third, inconsistent monitoring of features such as viral load and CD4 count lead to covariate missingness. This paper presents an all-in-one approach for both predicting HIV retention and optimizing scheduling while accounting for these complexities. We formulate and identify causal retention estimands in terms of potential return-time under a hypothetical scheduling decision. Flexible Bayesian approaches are used to model the observed return-time distribution while accounting for competing and censoring events and form posterior point and uncertainty estimates for these estimands. We address the urgent need for data-driven decision support in HIV care by applying our method to EHR from the Academic Model Providing Access to Healthcare (AMPATH) - a consortium of clinics that treat HIV in Western Kenya.