Yes absolutely Ethereum can be shut down.
It would not be easy though.
One way to shut Ethrereum down would be to turn off every computer running the software and delete every trace of all software versions. (Not very realistic)
Another way would be to use the power of media to turn the community against itself and once the rot sets in it would go into a downward death spiral until barely a sign was left of its existence.
Ethereum could become obsolete if a competitor offers more features or security that renders Ethereum practically useless in comparison.
Ethereum suffers multiple major security threats (afterall it is far more complex than bitcoin).
The state labels Ethereum as a terrorist tool and outlaws its use. Any citizen found using it to connect to the network would be fined and beaten to until submission.
Internet Kill Switch
Governments (or companies through TTIP) shut down the internet and restricts traffic to only those companies and entities who apply for and are granted an internet license (thank god for good old regulation!).
To shut down the internet the State would need a good dammed excuse. Terrorists hacking and stealing millions from bank accounts would be strong enough rationale for people to submit to the new regulated internet.
Meanwhile Arise Mesh Networking and community local networks and coins.
What do you think? let us know.