OTL, the Democrats controlled the Presidency from 1933 to 1953. What if they stretched this dominance out another decade?
Perhaps if Eisenhower accepted Truman's offer of an Eisenhower-Truman ticket in 1948, that could stretch things out. Then VP Truman comes back in 1956.
Roosevelt: 1933 - 1945
Truman: 1945 - 1949
Eisenhower: 1949 - 1957
Truman: 1957 - 1965
Honestly I don't think this is feasible. 32 years straight would be longest that any one party has controlled the White House. In a free and fair democracy that is unlikely to happen. Remember that Truman only won in 1948 because the Republicans took the election for granted and this allowed him to narrowly win in an upset. Once the economy inevitably enters recession it will hurt the incumbent party, and in this case it would probably doom the Democrats after over two decades in the White House. If not 1949 or 1953, then certainly 1958 would see a recession that sees the Republicans returned to power. I doubt Truman becomes President again in this scenario, and if the Democrats somehow eek out a win in 1956 they are done in 1960 due to the poor economy.
But that said, I do agree that Eisenhower in 1948 is a good way to prolong Democratic control past 1952. Here is my take:
32. Franklin D. Roosevelt (1933-1945), D-NY
33. Harry S. Truman (1945-1949), D-MO
34. Dwight D. Eisenhower (1949-1957), D-NY
35. Adlai Stevenson (1957-1961), D-IL
36. Nelson Rockefeller (1961-1969), R-NY
Truman gets sick of the Vice-Presidency and in 1952 he declines to seek re-election. A deadlocked 1956 convention nominates Illinois Governor Adlai Stevenson, who defeats Richard Nixon in the general election. Yet once the economy tanks Stevenson's popularity plummets and he loses to Rockefeller in 1960.
This is 28 years, not 32, but more feasible IMO.