I find there to be little reason to doubt Whittaker's explanation that he "reached a point of physical exhaustion from the great volume and continuous stresses" of serving on the Supreme Court, with an important aside that Whittaker also suffered from some form of anxiety and depression or other psychological condition that had previously impacted his work and life. His own secretary had told Whittaker's clerks that he previously suffered nervous breakdowns during his time as a lawyer before his appointment to the judiciary. Whittaker's nervous breakdowns and exhaustion were almost certainly exacerbated by his work ethic and judicial philosophy. Whittaker detested the (factual) notion that it was the clerks who did most of the research and opinion writing for their Supreme Court Justices and he instead chose devoted a significant amount of time himself to each case, with Chief Justice Earl Warren noting that "His entire preoccupation was with the law. He refused to leave time for any diversion." Other justices who served with Whittaker further commented on his perfectionism and hardworking nature, lending credence to his claims of exhaustion. Furthermore, Whittaker was infamous for not having a rigid political philosophy or strong ideological convictions regarding his cases, much to the distaste of legal scholars and to his own detriment, as he was frequently unable to come to a decision on the cases argued to SCOTUS, oftentimes regretting his choices once made.
Whittaker's precarious mental state was well known to those on the court as well as his family, as Justice Burton wrote in 1957 that Whittaker was on the edge of a mental breakdown even during his first year as a Justice, and in March 1962 his son prevented Whittaker from preparing for a suicide attempt. While Whittaker's propensity for nervous breakdowns was well-known by the court, his hospitalization in March apparently panicked Earl Warren, who in tandem with Whittaker's doctors persuaded him to retire.
The Press itself reported on the news of Whittaker's retirement rather dispassionately, echoing Whittaker's explanation of mental exhaustion and an over-bearing workload while emphasizing that the retirement was on "doctor's orders." There was little to no speculation regarding the nature of Whittaker's mental illness, and most of the articles surrounding the retirement instead focusing on who Kennedy would choose as a replacement. Similarly, there is not much information on the Kennedy Administration's reaction towards the retirement, thought it was a boon to Kennedy that he could replace the conservative Whittaker with a Democrat. In the years prior to the 1962 breakdown, Eisenhower's Attorney General William P. Rogers did have to convince Whittaker not to retire from the court.