Introduction: Bank failure prediction is an extreme rare-event risk-modeling problem in which overall accuracy can conceal weak identification of vulnerable institutions. While most prior early-warning research relies on linear statistical methods, these approaches may fail to capture complex, interacting risk thresholds. This study tests whether nonlinear machine learning improves prospective U.S. bank-failure ranking relative to transparent statistical benchmarks, explicitly accounting for the exceptionally low natural base rate of failure. Methods: This research utilizes public FDIC regulatory financial and failure records to construct a quarterly panel covering 11,235 institutions from 2001Q1 through 2025Q4. An L2-regularized logistic regression, a one-quarter hazard logit compounded to four- and eight-quarter horizons, and a fixed-parameter XGBoost model are evaluated in expanding-window annual tests with fold-specific preprocessing. Primary outcomes are annual-block precision-recall area under the curve (PR-AUC) and recall within the highest-risk 1% of bank-quarter observations. Test-size-weighted means are reported across 13 event-containing blocks alongside 1,000 paired annual-block bootstrap replications. Four targeted XGBoost sensitivity variants alter class weighting or tree depth. Results: XGBoost achieved mean PR-AUCs of 0.438 at both horizons, versus 0.352 and 0.335 for regularized logistic regression. At the top-1% cutoff, XGBoost recalled 75.9% and 66.8% of positive bank-quarter observations. Mean PR-AUC differences versus logistic regression were 0.086 (95% CI, 0.049-0.120) and 0.103 (0.053-0.146). All five XGBoost specifications retained positive PR-AUC differences with 95% intervals excluding zero. The class-weighted baseline had worse Brier scores than both logit benchmarks, and its raw scores are not population failure probabilities. Conclusions: XGBoost adds robust rank-ordering value for bank-risk triage under temporal out-of-sample evaluation. It is best interpreted as a prioritization tool; absolute probability use requires separate calibration and validation.