Maybe a giant net that pops out and messes it up before it reaches the tank...
Or maybe a big airbag made of kevlar or something that inflates when it sees the missile coming...
Or maybe a horde of drones that hover over the tanks and shoots the missiles down...
Or maybe each tank has a blimp attached to it that holds up a screen or something...
Or maybe the tank formations include drone tanks, that are just empty shells that look like tanks, with some kind of enticement about them that says "SHOOT ME"...
Or maybe some kind of DE beam or laser hooked up to a really fast phased-array radar system to shoot the missiles down... no one has asked me though...
Or, like you suggested, maybe at a point the Generals will just throw up their hands and say "This just ain't gonna work any more."
Excellent post.
Really good future countermeasures thinking. Brainstorming yields good ideas. Not all, but you never know what might actually work.