In analogy to the friction ridges of a human finger, the functional connectivity patterns of the human brain can be used to identify a given individual from a population. In other words, functional connectivity patterns constitute a marker of human identity, or a brain fingerprint. Notably, very little is known about whether brain fingerprints are preserved in brain ageing and in the presence of cognitive decline. Using fMRI data of 96 memory clinic subjects, here we show that individuals functional connectivity profiles remain unique even when cognitive impairment occurs. Yet, the patterns of functional connectivity that make the healthy subjects more identifiable change during cognitive decline, suggesting that the brain undergoes functional reconfiguration. Notably, the functional connections that were the most reliable in healthy cohorts disappeared during cognitive decline, leaving room for other stable connections, adapting to the process of neurodegeneration. We believe that these findings could help in moving towards a more personalised medicine and treatment during cognitive decline, and we hope they will set the ground for clinical fingerprinting of brain disease.