It can't be shutdown if the means are there, if the means are superior from the attacker than the target, then it can remain permanently offline. Talking from experience.
I have personally been involved with law enforcement in foreign countries that have raided houses with shotguns and flash bangs against Command and Control (C2) infra.
BGP FlowSpec helps a lot to prevent shunting the target IP/route completely, it's not as bad as the old days.