A diverse array of T cells is required for defense against pathogens. The naive CD4 T-cell repertoire reaches its peak diversity by early human adulthood and is maintained until older age. Surprisingly, around age 70, this diversity appears to plummet abruptly. A similar qualitative pattern holds for the CD4 T memory-cell population. We used mathematical models to explore different hypotheses for how such a loss of diversity might occur. The prevailing hypotheses suggest that the loss of diversity is due to a decline in emigration of cells from the thymus or a contraction in total number of cells. Our models reject these mechanisms because they yield only a gradual and minimal decline in the repertoire instead of the observed sudden and profound decrease later in life. We propose that an abrupt decline in the repertoire could be caused by the accumulation of mutations (defined here as any cell-intrinsic heritable event) that provide a short-term fitness advantage to a small number of T-cell clones (e.g., by an increased division rate or decreased death rate), with the person as a whole incurring the long-term cost of a decreased ability to fight infections.