I don't think Shastri is going anywhere, not until the end of WC 2019. And if we end up winning it he'll be there for a few more years or eternity. It's more to do with keeping everything smooth by not experimenting and risking the World Cup by changing the management all a sudden, who knows the current set of players barring a few like Pujara have a good rapport with him; likes of Rahul, Kohli, Pandya, etc. Second would be we don't have another stable option as of now to replace him and why would they if the players and the captain are happy.
It's pretty clear our legendary ex-cricketers like Ganguly don't like him either, haven't heard Sunny Gavaskar speak good about him plus it's evident Indian fans are no fan of the guy. Recently I've also seen the fans and media pressure making them change decisions; basically what's been written on social media having some effect on the final decisions.
People want Shastri to be sacked but that's the decision that can be taken only by the top officials who'd require a very solid reason to fire him before his term ends which they don't clearly have. You can't say sack him just so he speaks crap. They need to have a valid reason.