Unraveling the mysteries of how humans effortlessly grasp speech amidst diverse environmental challenges has long intrigued researchers in systems and cognitive neuroscience. This study delves into the neural intricacies underpinning robust speech comprehension, giving a computational mechanistic proof for the hypothesis proposing a pivotal role for rhythmic, predictive top-down contextualization facilitated by the delta rhythm in achieving time-invariant speech processing. We propose a Brain-Rhythm-Based Inference (BRyBI) model that integrates three key rhythmic processes - theta-gamma interactions for parsing phoneme sequences, dynamic delta rhythm for inferred prosodic-phrase context, and resilient speech representations. Demonstrating mechanistic proof-of-principle, BRyBI replicates human behavioral experiments, showcasing its ability to handle pitch variations, time-warped speech, interruptions, and silences in non-comprehensible contexts. Intriguingly, the model aligns with human experiments, revealing optimal silence time scales in the theta- and delta-frequency ranges. Comparative analysis with deep neural network language models highlights distinctive performance patterns, emphasizing the unique capabilities of our rhythmic framework. In essence, our study sheds light on the neural underpinnings of speech processing, emphasizing the role of rhythmic brain mechanisms in structured temporal signal processing - an insight that challenges prevailing artificial intelligence paradigms and hints at potential advancements in compact and robust computing architectures.