Answer:
Democrats held power for so long in the 30s, 40s, and 50s because the Republican Party was seen as responsible for leading the United States to the Great Depression.
The Great Depression was seen a direct result of the economic policies of the Republican Party, which adopted laissez faire policies during the 10s and 20s. In particular, the presidency of Herbert Hoover led to a great loss of social support to the Republicans.
This, added to the fact that the Democrats led a period of great economic recovery after the crisis (Roosevelt's New Deal and Johnson's Great Society) made the Democratic Party the dominant political party in those years.
