Do you think Hinduism will survive in the coming few centuries?

Hare Krishna will survive, and in the near future become the leading world religion.

It is an observable fact that time ends all things. Time has a corrosive effect on everything. Time makes you grow old and die. Time kills all living entities. Same with knowledge. If the knowledge is not carefully preserved in a line of teachers, it will disappear in due course, simply from the effects of time.

Krishna says:

I instructed this imperishable science of yoga to the sun-god, Vivasvan, and Vivasvan instructed it to Manu, the father of mankind, and Manu in turn instructed it to Ikshvaku. —Bg 4.1

This supreme science was thus received through the chain of disciplic succession, and the saintly kings understood it in that way. But in course of time the succession was broken, and therefore the science as it is appears to be lost. —Bg 4.2

That very ancient science of the relationship with the Supreme is today told by Me to you because you are My devotee as well as My friend and can therefore understand the transcendental mystery of this science.—Bg 4.3

Time on earth passes through four ages, lasting together 4,32 million years. During this time, things will gradually deteriorate, until now, in Kali-yuga, where everything has degraded to the extent where knowledge of the Truth is all but completely lost.

Fortunately, due to the glorious efforts of Srila Prabhupada and his ISKCON, which are the direct descendents of the bhakti-revival movement begun by God Himself, Chaitanya Mahaprabhu, 500 years ago, Sanatan-dharma is now spreading like wild-fire all over the world. This only happens once in a day of Brahma, once every 1000 Kali-yugas, or every 4 billion years, so it’s an extremely rare occurrence.

Kali-yuga is the present age of quarrel and hypocrisy. The age of Kali began 5000 years ago, after Krishna left the planet.

Kali-yuga is a period of time where evil people can have their desires for political power and dominance fulfilled. God allows that, so that sinful people can get the karmic reactions, they are due.

Srila Prabhupada once stated in a lecture given in Los Angeles - the very fact that you have taken birth in Kali-yuga means you are very, very, very sinful.

However, the present Kali-age is one out of 1000 Kali-yugas, where God personally descends to planet Earth to display His pastimes and deliver Bhagavad Gita. And when ever Krishna descends, He comes again 4500 years later as Chaitanya Mahaprabhu, to deliver people by the Hare Krishna mantra.

So in this particular Kali-yuga, which only happens once in a day of Brahma, or every 4 billion years, there will be a golden age of 10.000 years of Krishna consciousness. That period began 500 years ago with the descent of Chaitanaya Mahaprabhu in West Bengal.

It’s a work in progress. though, and it’s only going to get worse before it gets better. Nature, obviously, has to rid herself of the present ungodly consumer culture before the Golden age can really take root.

Srila Prabhupada has stated that one day people will thank the Hare Krishnas for saving the world.

Vishnu says:

When one resents the demigods, who represent God, the Vedas, which give all knowledge, the cows, brahmanas, Vaisnavas and religious principles, and ultimately Me, the Supreme, he and his civilization will be vanquished without delay. -- Srimad Bhagavatam 7.4.27

In the Brahma-vaivarta Purana, in a conversation with Ganga Devi, Lord Krishna describes that after 5,000 years of Kali-yuga have passed, a great sage and worshiper of Krishna's holy names, will appear and spread the chanting of the Hare Krishna mantra not only in India but throughout the world.

Krishna says:

After the first 5,000 years of Kaliyuga has elapsed, a pure devotee will be born, and he will spread the chanting of Krishna’s holy names all over the world. (Brahma Vaivarta Purana)

And it was also foretold by Bhaktivinode Thakur a hundred years ago:

Very soon the unparalleled path of hari-nama sankirtana will be propagated all over the world. Oh, for that day when the fortunate English, French, Russian, German, and American people will take up banners, mridangas, and karatalas and raise kirtana through their streets and towns! When will that day come? (Srila Bhaktivinoda Thakura Sajjana Tosani 4.3, 'Nityadharma Suryodoy' 1885)