The ability to store, integrate, and manipulate information declines with aging. These changes occur earlier, faster, and to a greater degree as a result of neurodegeneration. One of the most common and early characteristics of cognitive decline is difficulty with comprehension of information. The neural mechanisms underlying this breakdown of information processing are poorly understood. Using functional MRI and natural stimuli (e.g., stories), we mapped the neural mechanisms by which the human brain accumulates and processes information with increasing duration and complexity in participants with amnestic mild cognitive impairment (aMCI) and healthy older adults. To explore the mechanisms of information processing, we measured the reliability of brain responses elicited by listening to different versions of a narrated story created by segmenting the story into words, sentences, and paragraphs and then scrambling the segments. Comparing healthy older adults and participants with aMCI revealed that in both groups, all types of stimuli similarly recruited primary auditory areas. However, prominent differences between groups were found at the level of processing long and complex stimuli. In healthy older adults, parietal and frontal regions demonstrated highly synchronized responses in both the paragraph and full story conditions, as has been previously reported in young adults. Participants with aMCI, however, exhibited a robust functional shift of long time scale processing to the pre- and post-central sulci. Our results suggest that participants with aMCI experienced a functional shift of higher order auditory information processing, possibly reflecting a functional response to concurrent or impending neuronal or synaptic loss. This observation might assist in understanding mechanisms of cognitive decline in aMCI.