it is true that Buddhism was already in steady decline at the time of
muslim invasion to North India. A study of South Indian history would
points that out. That was mainly due to the resurgence of Brahmanism,
the renewed interests in certain Brahmin practices such as tantric
practices, and its adaptation by the rising Vajrayana school had
caused a blurring of lines between Buddhism and Brahmanism.
The ruthless muslims only make the end came quicker, and possibly
destroying bulks of Sanskrit literature now available only in Chinese
and Tibetan. The British colonisation, the civil strife and social
unrest didn't help much.
The term Hinduism actually makes things worst, like Taoism in China,
it *can* refer to all indigenous religious practices in India,
bringing Buddhism and Jainism under its fold. That is why visitors to
country like Bhutan and Nepal will learn from the locals that
Hinduism and Buddhism are actually *the same*.
[It may be interesting to know that, throughout history, Buddhism is
a religion that does not perform well in turbulent times. This is
probably due to Buddha's message of compassion and wisdom. For
example, in China, alternative views such as Taoism and Confucianism
always take precedence during wartimes. On the other hand, in the
prolonged period of peace and prosperity in the Tang dynasty,
Buddhism flourished with eight major schools, each with many sects
and branches.]