The deployment of multimodal models in high-stakes domains, such as self-driving vehicles and medical diagnostics, demands not only strong predictive performance but also reliable mechanisms for detecting failures. In this work, we address the largely unexplored problem of failure detection in multimodal contexts. We propose Adaptive Confidence Regularization (ACR), a novel framework specifically designed to detect multimodal failures. Our approach is driven by a key observation: in most failure cases, the confidence of the multimodal prediction is significantly lower than that of at least one unimodal branch, a phenomenon we term confidence degradation. To mitigate this, we introduce an Adaptive Confidence Loss that penalizes such degradations during training. In addition, we propose Multimodal Feature Swapping, a novel outlier synthesis technique that generates challenging, failure-aware training examples. By training with these synthetic failures, ACR learns to more effectively recognize and reject uncertain predictions, thereby improving overall reliability. Extensive experiments across four datasets, three modalities, and multiple evaluation settings demonstrate that ACR achieves consistent and robust gains. The source code will be available at https://github.com/mona4399/ACR.