Rupert Murdoch is showing symptoms of the same affliction. The news that Lachlan, his eldest son and presumed heir, has quit News Corporation for a quiet life in Australia means James, the BSkyB boss, is now the only junior Murdoch contender.
Lachlan's decision has also prompted his father to reassert that his own retirement has been put on hold "forever". "Indefinitely" may be a more accurate word but, then again, you never know with the Murdochs (Rupert's mother, Dame Elisabeth, is fighting fit at 96).
My guess is that, health permitting, Rupert will carry on until he is 80, five-and-a-bit years away. Even tireless control freaks are ultimately at the mercy of the years and it would be hard for anyone to run a global media empire in their ninth decade. More importantly, it will give James, still only 31, some time to mature. He has quietly impressed during his short tenure at BSkyB; he has a cool mastery of detail and a thoughtful head on his shoulders.
But a further five years' apprenticeship will do him no harm.
Although deeply unfashionable and increasingly rare, family-dominated media businesses have a good track record. Associated Newspapers is in the assured hands of yet another Rothermere, who is also a stripling in his 30s. Campaign's publisher, Haymarket, owned by Lord Heseltine and his family, is another example and there is no hint yet that the seventysomething proprietor will retire to tend his arboretum.
Perhaps a family-run business puts more rather than less pressure on each generation to deliver. After all, you don't want to be the chump who ruined the company your overachieving predecessors built up.
Whatever happens, the Murdoch dynasty appears secure and canny old Rupert has a further insurance policy in the shape of his two-year-old daughter, Chloe. Now, that would mean he could go on until he is at least 105.