Roman paganism and later Germanic/Slavic/Baltic paganism crumbled after the ruling class converted to Christianity. After conversion the bulk of the populace remained pagan however European paganism seemed to gradually crumble under the organised and dogmatic approach of a monotheistic religion. India was ruled by Muslims for centuries (Mughals etc.) yet the polytheistic "pagan" religion survived despite efforts to convert them. What was the difference here? Why did Hinduism survive whilst European polytheistic religions crumbled?
I would like to point out that considering Hinduism a polytheistic religion is a common misconception. Hinduism is a monotheistic religion. The different 'gods' (they're refereed to as 'devs' in Sanskrit; the closest translation is 'gods', but it's not entirely accurate.) are meant to symbolize different forms and shapes of the Brahman- the eternal cosmic force that unites all diverse forms of the universe. In other words, a cosmic force, or entity- or God with a capital G if you want to consider it so.
That said, many Mughal emperors, especially Akbar, sought to smooth Hindu- Muslim relationships and adopted very tolerant policies to other religions. It's also a mistake to say that Mughals were completely dominant over the Indian subcontinent throughout the entire rule as there were many Maratha and Rajput kingdoms opposing them. That, combined with the sheer population of Hindus in one of the most populated regions of the earth, as well as a resilient mentality, Hinduism continued to thrive under oppression.