First of all, there was a period of dictatorship in India, Indian Emergency of 26 June 1975 – 21 March 1977 and, after that, there was a minor civil war with the Sikh minority. There was also considerable religious unrest during the formation of the nation. So, I wouldn't say that Indian culture precludes these political activities.
I would say that one major reason was the nature of the world during the bulk of India's history, namely, the Cold War and India's strategic location. It was in the interest of both the US and USSR to have a stable government in India where neither side had an upper hand. Therefore, there were no significant outside influences pushing for radical changes as there was in China and other countries.
Another factor was that India was underdeveloped and there was a great desire to see economic improvement. Having a stable, mostly democratic, government with good rule of law and protection of property rights is the best way to achieve this goal. India's leadership knew this and, but for a few exceptions brought on by typical human failings as I noted above, they've headed in this direction.