Will India ever split?

Will India ever split and if so, under what circumstances?

Very hard to do. It is not in Western interests to split India, ISI is too small for this task and Indian secession movements are too weak/incoherent to let this happen.

Western Interests:
First let us take the Western/CIA's interest in destabilizing India. Here is the region around India. US has fought all around India. From Iraq & Iran all the way in left to North Korea all the way in the right, this is the headache map for the US. It has had a cold war up north, trade war with China and there is a major war on Piracy going in Indian ocean. And on India's west lie two failed nations mired in terrorism. And on India's east lie a couple more almost failed regions such as Myanmar. 

The ONLY source of comfort for the US administration in this whole big region that holds more than two-thirds of world population is India that lie in the center. India is neither a failed nation like its western neighbors nor a non-democratic power that can challenge US in a military sense like its northern peers. India is strong enough to be a major ally, but weak enough to not be a major rival.

If India were to destabilize and collapse, American operations in Asia could go to drainage as there is no way to manage a 1.2 billion region if you can't even manage a 50 million region. There is enough of the dangerous, failed "___stans"  to warrant a Khalistan or Kashmiristan. Thus, US will do everything to avoid destabilizing India - even assuming it could. 

Indian secession movements:

1. Northeast separation movements - There are separatist elements all over India's north east - most notably in Assam, Tripura and Nagaland. Although the secession demand is strong, it is quite impractical to create new nations as individual tribes in the region cannot get along with each other. See more here: Should the North Eastern states of India try to secede from India? Since every tribe wants to autonomous, there is no way to create a separate nation for them.
2. Naxalites - This is a group of communist revolutionaries who try to revive the failed ideas of Lenin and Mao. This is a very serious threat in India's interior and the rampant corruption + scant development has given huge ammunition to the lunatics. Although these groups cannot create a separate nation on their own, they can do enough harm by destabilizing India's interior.
3. Punjab Khalistan movement - At one point the most feared movement in India. Although it had some traction, the viability of a new land-locked state amidst two power nuclear nations was always questionable. Given that most of the Sikhs are also quite patriotic & attached to India, the movement eventually petered out.
4. Kashmir separatism - A big threat at one point, but now has gone out of steam as Kashmiri people have realized that India is not going to give up easily and Pakistan is not that sexy either. Staying independent inbetween 4 nuclear nations is even more difficult.
5. Dravidanadu - Some crackpots in the 1940s-60s thought South India was run over by "Brahmins" and want to secede from India due to that. It had some steam initially, but eventually the cracks got too big as people found out that hating one minority community is not a good enough reason to create a new nation. Has almost zero influence in Tamilnadu today.

None of the 5 major movements can build a viable nation independent of India. The movement founders all hate India, but don't give a credible alternative to their followers. 

Pakistan's and China's actions:
On surface, it is in the interest of both China and Pakistan to split their main rival - India. Although it is alleged that China arms some of the Northeast rebels, Chinese leadership is also aware of the Frankenstein monster that it could unleash given that its two most troubled regions - Xinjiang and Tibet lie adjacent to India's problem regions of Kashmir and North east. Any major support of an armed rebellion in India could quickly go contagious into those Chinese regions and give their people bigger dreams. So, China has not taken a major step given their own interests. 

Regarding ISI - Pakistani intelligence, for all about its hype in India, it is too small to create any major havoc. It can detonate bombs & can cause some destruction, but it is very hard to convince Indians of various regions to go separate.

Risks India face
1. Weakening of federal institutions. India has always had very respectable federal institutions - Supreme Court, Reserve Bank of India, Army and Indian Railways that most Indians believe to be fair and worthy. In contrast, the state institutions - including the high courts, police and state governments, get very little respect. If state were to get more power, then we would face really unfair/corrupted state instituitions of a few major states dictating more terms. This can destabilize India.

2. Religious tensions. This is an issue for India post the bloody partition in 1947. Given the multitudinous religions with troubled history we constantly face a threat of major riots. Indian governments have not done much to appease both the majority and the minorities.

3. Water wars. This is a really serious issue, especially in the South. Although it might not split India, it can serious harm India's federal nature. 

Although all these risks are credible, overall they have not gone to a point of being a major threat. 

Final:
In summary, India has no major threat to sovereignty right now. The bond of "Bharat" is quite strong and most Indians are quite proud of staying together in spite of constant teasings and minor tussles with other states. Moreover people have understood that any Balkanization will make the "water wars" between the states even more terrible and will bring Indian to the nadir that we had just before the British invasion in 18th century.