(1) Background: The adjustable transobturator male system (ATOMS) device serves to treat post-prostatectomy incontinence, as it enhances residual urinary sphincteric function by dorsal compression of the bulbar urethra. We investigated the clinical parameters affecting continence recovery using this device and developed a decision aid to predict success. (2) Methods: We reviewed consecutive men treated with first-time ATOMS for post-prostatectomy incontinence from 2014 to 2021 at our institution. Patient demographics, reported pads per day (PPD), 24-h pad-test and Standing Cough Test (SCT), results’ grades 1–4, according to Male Stress Incontinence Grading Scale (MSIGS), and the International Consultation on Incontinence Questionnaire-Short Form (ICIQ-SF) questionnaire were assessed. Treatment success was defined as no pads or a single PPD with ≤20-mL 24-h pad-test. Logistic regression was performed using a stepwise model (entry 0.15 and stay criterium 0.1) to evaluate independent variables’ determinant of dryness. Receiver-operating characteristic (ROC) curves for predictive variables were evaluated and their area under curve (AUC) was compared. A nomogram was generated and internally validated to predict probability of treatment success. (3) Results: Overall, 149 men (median age 70 years, IQR 7) were evaluated with a median follow-up of 45 months (IQR 26). Twelve patients (8%) had previous devices for incontinence, and 21 (14.1%) had pelvic radiation. Thirty-five men (23.5%) did not achieve continence after ATOMS adjustment (use of no or one security PPD with ≤20-mL 24-h pad-test). In univariate analysis, Charlson comorbidity index (p = 0.0412), previous urethroplasty (p = 0.0187), baseline PPD (p < 0.0001), 24-h pad-test (p < 0.0001), MSIGS (p < 0.0001), and ICIQ-SF questionnaire score (p < 0.0001) predicted ATOMS failure. In a multivariable model, 24-h pad-test (p = 0.0031), MSIGS (p = 0.0244), and radiotherapy (p = 0.0216) were independent variables, with AUC 0.8221. The association of MSIGS and 24-h pad-test was the superior combination (AUC 0.8236). A nomogram to predict the probability of ATOMS failure using the independent variables identified was proposed. (4) Conclusions: Several variables were identified as predictive of success for ATOMS using clinical history, physical examination (MSIGS), and factors that evaluate urine loss severity (PPD, 24-h pad-test, and ICIQ-SF questionnaire). MSIGS adds prognostic value to 24-h pad-test in assessing success of ATOMS device to treat post-prostatectomy incontinence. A nomogram was proposed to calculate the risk of ATOMS failure, which could be of interest to personalize the decision to use this device or not in the individual patient.