Hood commissioned in 1920 and got a deep refit for six days short of two years long at Portsmouth (June 1929 - May 1931), including extensive repairs to hull, machinery and equipment.
Otherwise put, Hood needed a long refit after about nine-ten years of service. Counting forward this can mean that her next refit would be needed somewhere around 1940, probably a bit sooner as she was aging. And by 1939 she was indeed starting to show signs of wear and a machinery replacement was seen as necessary in the near future, but by then Renown, Valiant and Queen Elizabeth were being reconstructed so there was no free place in the deep refit schedule. It was estimated that she could last until 1941 if nursed along which would work out for a 1939-1940 start of rebuilding. But I'm guessing this was based on peacetime steaming, not wartime tempo.
Her powerplant was not worn out by 'interwar showing the flag', it was a combination of age and it being nine years since her machinery had gotten its mid-life refit. Hood was hardly left alone after 1931 - she received smaller refits and modernizations: two weeks in 1932, one month in summer 1934, three and a half months in 1936, a month and a half in 1937, another month in 1938, seven months in 1939, two months in 1940 and finally two more months in 1941. This did not involve major engine repairs which were not necessary until 1939 or so, and in late 1939 the war broke out.
Ironically, if her machinery had started playing up in 1935-1936, one of the other ships would have forfeit their turn and Hood would have gotten a rebuilt instead. But at that point she was smack in the middle between major refits. She would simply have gotten the next spot for rebuilding in 1939-1940 when she was due for a major refit anyway.