In business, even in the US, there is almost never loyalty. Or, perhaps more precisely: In business, you have to buy loyalty.
I guarantee that there is a price at which you could buy a very stable, very competent team in India. But then it wouldn’t be super cheap outsourcing any more, and the benefits aren’t so great.
If you want stability in your workforce, you gotta pay for it. Whether in cash, working conditions, or some other way.
Pay for cheap labor, get cheap labor. And don’t be surprised or disappointed that you got it.