Looks like it was 31 December of the year in which he turned 60. Here are some quotes from The New York Times, reporting on the retirements of several White Star captains in the 1929-1931 time frame:
17 December 1929: Captain Walter H. Parker, R. N. R., master of the White Star liner Olympic, will make his final entry into New York harbor in the company's service when he arrives tomorrow morning. He retires when the liner arrives at Southampton on Dec. 27, having reached the age of sixty years.
3 December 1930: Captain James Kearney, one of the senior shipmasters in the White Star fleet, brought the Adriatic into this port yesterday for the last time. After he docks at Liverpool he will retire, having reached the age of 60.
4 December 1930: A matter of two days in the sailing time of the White Star liner Olympic will cause her master, Captain George E. Warner, to retire when she reaches Southampton Dec. 12, it was learned yesterday on the arrival of the ship. ... The rules of the White Star line require that a master retire in the year of his sixtieth birthday, which Captain Warner observed recently. The next sailing of the Olympic from New York on Dec. 27 would take his service over into 1931, as the vessel would not reach Southampton until Jan. 2.
6 December 1931: Two veteran sea captains closed their careers during the past week so far as the port of New York was concerned. Captain Evan Davies took the White Star liner Baltic out from her North River pier on Friday night, knowing that on arrival in Liverpool he would be placed on the retired list because he had reached the age of 60.
oh my goodness! I completely missed this posting. Anyway the Captain James Kearney, named in Mark's reply, was my Great Grandfather. According to his Niece (who knew him very well and lived with him around the time of his retirement)Retirement at 60 was mandatory due to the depression.
In the newspaper reports, that I have, it states that Adriatic's Chief Engineer J.A. Mungall also retired when the Adriatic docked after that voyage.
Some time ago I got the confirmation on the case I was working on - the man also retired in the year he turned 60. So while that's correct, it was not in December; but quite at the beginning of the year. Perhaps he requested an earlier retirement?