I believe the Yankees had a pretty good run starting in 1949 through the 50s. Cant remember the Word Championship winner. But in the 12 years from 1949-60 they made the Series 10 years. (only times they lost the AL pennant Cleveland-1954, White Sox-1959, and in 1954 the Yankees won 103, which was the record I think for a non-pennant winner at the time)
I think Yogi Berra was the only player on the team through that entire time, however. Though, I think Hank Bauer was there through 1958 or 1959. Casey Stengel was the manager those 12 years and only those 12 years for the Yankees.