A new state in India?

India has created a new state by splitting the large southern region of Andhra Pradesh. Several ministers have resigned in protest. (A note: be careful reading the linked article: the way it’s written seems to imply that part of southern India just became a new country, which it didn’t. Basically, it would be like Texas, or California, being split into two states by the federal government.)

Is there a good justification as to why some areas of regions, seeking autonomy or independence, succeed in political demands, and other areas don’t succeed? What prevents some separatist movements, like the Basque (to take just one example), from succeeding, while others do not fail in their demands?