I'm a way outsider and not as studied as I would like on India, but my question is "why hasn't India broken up further?".
If by "further" you refer to 1947 division of the subcontinent then it has in fact broken up again, in 1971 when East Pakistan became Bangladesh.
There is great value in being united of course, which is also the original intention behind the EU. When constituent states disagree or want to split up, like Telangana and Andhra Pradesh did recently, they can do it through a constitutional process rather than a war. Being a larger state also provides greater opportunities for its citizens.
As time has passed, the part called "India" today has faced a few separatist movements, but has held together primarily by creating a more successful shared narrative so it means something to be "Indian" in addition to being a Punjabi or Gujurati or Muslim, Hindu or Jain. This is likely to continue.
Within today's India, there was first Tamil separatism, then Sikh, Kashmir and then a few small eastern tribal groups. They have each waxed and waned over the years for different reasons. Ultimately it is the duty of the Indian state to preserve & strengthen the Union while ensuring that its value for each constituent outweighs any ethnic or religious separatist sentiments.
The US is unique in being formed basically from scratch, and growing from there, rather than as a merger of historical nation/states.
It just seemed like our Civil War shutdown the separatists and India separatists had some success, so I was wondering if there is a likely further break or not.