The answer is rather complex. Roosevelt and his life-long ally, Henry Cabot Lodge, were very effective campaigners. In those days, candidates still followed the principle which had held sway since the beginning of the republic to the effect that the office should seek the man, but that the man should not seek the office. So candidates would sit on the front porch and trade quips with the boys of the press, and active young men like Roosevelt and Lodge would go out to stump for the votes. They were both good at it, too. However, they were unwilling to campaign for James Blaine in 1884 because of the taint of corruption which surrounded him. Many other young Republicans also would not campaign for him, but Roosevelt and Lodge were well known and branded as Mugwumps (fence sitters, with their mugs on one side and "wumps" on the other).
Grover Cleveland won that election, and many young Republicans were OK with that, because he was seen as a reformer. Nevertheless, as party loyalists, Roosevelt and Lodge campaigned for Benjamin Harrison in 1888, and Harrison lost the popular vote but won in the Electoral College. Harrison appointed Roosevelt to the Civil Service Commission, where, to the horor of both parties, he began to ruthlessly clear out the dead wood while insisting on examination and experience on the part of applicants. He, even more than Lodge, had become the despair of the party. This feeling increased when Grover Cleveland returned to the White House in the 1892 election, and retained Roosevelt in his job.
For whatever anyone may allege against William McKinley, he was an honest man, and Roosevelt and Lodge campaigned vigorously and effectively for him in 1896. Roosevelt's pay-off was to be appointed Assistant Secretary of the Navy (he was always interested in naval affairs--his first book was The Naval War of 1812
, the standard work on the subject to this day). The Secretary, Mr. Long, was a weak reed, and was more than happy to leave the running of the department to Roosevelt. Roosevelt had already secured a promise that if war broke out with Spain, he would be allowed to resign his position and take a commission in the army. (He was Theodore Roosevelt Jr.
--Theodore Roosevelt Sr. had married Martha Bulloch of Georgia, and so did not take a commission during the Civil War out of regard for his wife's feelings. One of his uncles was a Confederate States naval officer in England who worked to acquire ships there, and a younger uncle was an officer under Rafael Semmes, who commanded one of those ships, CSS Alabama
. After the war, they stayed in Liverpool, and the family would travel there to visit them. Theodore Jr. idolized his uncles. Many biographers believe that that is why Roosevelt was so bellicose before the Spanish War. I personally believe that his experience of the Spanish War drained that bellicosity from him.)
McKinley's physician was Leonard Wood of the Army. McKinley would often chide Wood by asking him: "Well, Leonard, have you and Theodore declared war on Spain yet?"--to which Wood would respond something to the effect of "No sir, but we're hoping you will soon." After the Maine
incident, Secretary Long left the office for the afternoon, and Roosevelt fired off a series of telegrams to concentrate all available naval forces on the Gulf coast of Alabama and Florida, and to rush supplies to those ports. He then tendered his resignation, and helped to raise the First United States Volunteer Cavalry regiment--the "Rough Riders." Leonard Wood was given command as the Colonel, and Roosevelt was his executive officer with the rank of Lt. Colonel. In Cuba, Wood was given command of the brigade, Roosevelt taking command of the regiment. He was in command when Kettle Hill and San Juan hill were taken. That lead to the collapse of the Spanish, as San Juan hill dominated Santiago de Cuba, the capital.
After the war, Roosevelt was a shoe-in for the office of Governor of New York, once again, to the despair of the Republican powers that were. He immediately set out to root out corruption and "machine politics." The political boss of New York, Thomas Platt, wanted him out of New York, and managed to get him tapped as McKinley's running mate in 1900.
Men like Roosevelt and Lodge felt the party of Lincoln should work for the good of the common man, and should end corruption and machine politics. As President, he became the "trust buster" on the principle that corporations were robbing the common man. He groomed William Taft as his successor, and broke the rule about statesmen standing aloof from campaigns, assuring Taft's election.
But Roosevelt became convinced that Taft had betrayed the principles of the progressive Republicans. So, in 1912, he ran against him as an independent. To a point, it looked as though he might win--until he was shot. Although he survived the assassination attempt, he lost his shot at the White House. The result was that he siphoned off votes from Taft, and Woodrow Wilson won. (Even after being shot, Roosevelt came in second in the popular vote, but Wilson buried the other three runners in the Electoral College.)
The powers of the Republican party decided "never again." Young progressive Republicans were ruthlessly weeded out of the party. Anyone wanting a career in the party would have to toe the party line or leave. There have been "moderate" Republicans since that time, but no more progressive Republicans.