Many believe that Buddhism ceased to have a large following in India because it came under the attack of Sankara. This is not true. There are very few passages in the Acarya's commentaries critical of that religion, a religion that was opposed to the Vedas. Far more forcefully has he criticised the doctrines of Sankhya and Mimamsa that respect the Vedic tradition. He demolishes their view that Isvara is not the creator of the world and that it is not he who dispenses the fruits of our actions. He also maintains that Isvara possesses the laksanas or characteristics attributed to him by the Vedas and the Brahmasutra and argues that there can be no world without Isvara and that it is wrong to maintain that our works yield fruits on their own. It is Isvara, his resolve, that has created this world, and it is he who awards us the fruits of our actions. We cannot find support in his commentaries for the view that he was responsible for the decline of Buddhism in India.
Then how did Buddhism cease to have a considerable following in out country? Somebody must have subjected it to such rigorous attack as to have brought about its decline in this land. Who performed this task? The answer is the mimamsakas and the tarkikas. Those who are adept in the Tarka-sastra(logic) are called tarkikas. The Tarka is the part of Nyaya which is one of the fourteen branches of Vedic learning and which comes next to Mimamsa. People proficient in Nyaya are naiyayikas; those well versed in grammar are "vaiyakaranis"; and those proficient in the Puranas are "pauranikas".
Udayanacarya, the tarkika, and Kumarilabhatta, the mimamsaka, opposed Buddhism for different reasons. The former severely criticised that religion for its denial of Isvara. To mimamsakas, as I have said earlier, Vedic rituals are of the utmost importance. Even though they don't believe that it is Isvara who awards us the fruit of our actions, they believe that the rituals we perform yield their own fruits and that the injunctions of the dharmasastras must be carried out faithfully. They attacked Buddhism for its refusal to accept Vedic rituals. Kumarilabhatta has written profusely in criticism of that religion. He and Udayanacarya were chiefly responsible for the failure of Buddhism to acquire a large following in this country. Our Acarya came later and there was no need for him to make a special assault on that religion on his own. On the contrary, his chief task was to expose the flaws in the systems upheld by the very opponents of Buddhism, Kumarilabhatta and Udayanacarya. He established that Isvara is the creator of the universe and that it is he who awards the fruits of our actions.
I am mentioning this fact so as to disabuse you of the wrong notions you must have formed with regard to Sankara's role in the decline of Buddhism. There is a special chapter in one of Kumarilabhatta's works called "Tarkapadam" in which he has made an extensive refutation of Buddhism. So too has Udayanacarya in his Bauddhadhikaram. These two acaryas were mainly responsible for the decline of Buddhism in our land and not Sankara Bhagavatpada. What we are taught on the subject in our textbooks of history is not true.
For a general background, please see here