Loss to follow-up (LTFU) remains a major challenge in HIV care, particularly in resource-limited settings. While several studies have identified its predictors, many have neglected the competing risks of transfer out and death, as well as the dynamic influence of these predictors over time. A retrospective cohort study was conducted among adult HIV patients who initiated antiretroviral therapy (ART) between 2019 and 2024. LTFU was a primary outcome, whereas transfer out and death were competing risks. A Fine‒Gray subdistribution hazard ratio (SHR) regression analysis identified LTFU predictors within a competing risk framework. An extended SHR model with a time‒covariate interaction term was used to examine the predictors' time‒varying effects on LTFU risk. Data analysis was performed via STATA 17 and Python 3.9. In a cohort of 4,135 HIV patients (8,521.54 person-years of follow-up), the overall incidence of LTFU was 13.10 per 100 person-years (95% CI: 12.35-13.89), with cumulative risks of 15%, 25%, and 35% at 1, 3, and 5 years post-ART, respectively. The predictors of LTFU included younger age (15-24 years: aSHR = 1.51), male sex (aSHR = 1.24), incomplete address details (aSHR = 1.72), noninitiation/noncompletion of TPT (aSHR = 2.16), poor adherence (aSHR = 2.54), and undernutrition (aSHR = 2.03). While younger age (e.g., 15-24 years) was associated with an increased risk of LTFU at baseline (baseline aSHR = 1.36, p = 0.014), this association diminished over time (interaction aSHR = 0.54, p = 0.001). Undernutrition consistently predicted LTFU (baseline aSHR = 1.64, p < 0.001), with no significant time-dependent effect (interaction aSHR = 1.01, p = 0.903). In conclusion, this study highlights the high incidence of LTFU among HIV patients and its key predictors. Notably, age has a significant time-dependent effect, with its influence on the risk of LTFU being most pronounced during the early stage of ART initiation, whereas nutritional status remains a consistent predictor of LTFU over time.