Why was Martin Luther successful where others had failed?
I do not think that Luther's questioning of the church made him successful; it is more nearly correct to say that the timing of Luther's message, with the invention of the printing press and the political upheaval in Germany which gained him support from a number of princes, enabled his message to survive when others had not.
Any number of reformers had protested the abuses of the church, notably Jan Hus who was promised safe passage to the Council of Constance to defend his position and was rewarded for his efforts by being burned at the stake. The Brethren of the Common Life, led by Thomas a Kempis, had also urged that the life of Christ should be followed as the perfect example of Christianity.
Following Luther's issuance of his ninety five theses and his public debate with Johan Tetzel over the issuance of Indulgences, Pope Leo X had issued a papal bull, ExsurgeDomine ("Arise, Lord") which gave Luther two months to recant. Luther responded by burning the bull publicly. By the time of Luther's public response, the issue had transcended one of church reform and had become one of German nationalism, and thus gained more momentum than Luther ever dreamed. Many German princes supported Luther rather than Charles V, the Holy Roman Emperor, as they were thereby freed from the power of the Pope, which they resented. They did not do so from religious conviction; but rather from political expediency.
Leo X then issued a Bull of Excommunication Decet Romanum Pontificem ("it is fitting that the Pope") however Charles V called a special diet to consider the matter, the Diet of Worms, since he needed the support of the Lutheran princes to continue his war against the French and Turks.
It was at the Diet that Luther delivered his famous pronouncement:
Unless I am convinced by the evidence of the scripture or by plain reason—for I do not accept the authority of the Pope or the councils alone, since it is established that they have often erred and contradicted themselves—I am bound to the Scriptures I have cited and my conscience is captive to the Word of God. I cannot and will not recant anything, for it is neither safe nor right to go against conscience. God help me. Amen.
Luther was declared an outlaw and would have suffered the fate of Jan Hus; however Frederick, Duke of Saxony, protected him. This not only saved Luther's life, it gave him an avenue to publish his ideas.
More important than the support of the princes was the influence of the Printing Press, invented earlier by Johan Gutenberg. Luther's writings were spread throughout Germany written in both Latin and German. Since previous writings had been only in Latin, the inclusion of the vernacular German meant that few people who could read were not exposed to Luther's ideas. It is highly doubtful that Luther would have attained the success which he did were it not for the influence of the printing press.
Part of the reason why Luther was so successful was that his premise of questioning the church was something that resonated with so many people. Luther's questioning struck at the very heart of religious worship. If one possesses a true sense of belief in spirituality, what happens when this collides with questioning the political institution that is meant to "lead" devotees on the path of spiritual worship? Luther's questioning about the sale of indulgences and the practices of the church, in general, resonated with individuals because it helped to establish the idea that the political leadership of the church might not be directly embracing its spiritual ends. Luther's success resided in the elemental nature of his questioning and the debate that arose from it. Given the fact that Luther emerges at a time when more people were reading Scriptures and that his critique of the church practices resonated with so many who struggled between individual worship and questioning the practices of the church leadership, Luther struck a chord with people, allowing their own beliefs and thoughts to be resonated with him. Nothing like it had been experienced prior because of the combination of time and context within which Luther was a part.