It's already known that bitcoins don't have any official community to look after. So the bitcoin wallets which we use aren't governed by any one too. They are working independent on their own without anyone to point finger at them for any reason.
So, if you are using any bitcoin wallet from any provider and it gets shut down , then unfortunately you do lost your bitcoins. You can't do anything about it. Just make sure that you use a reliable and trusted wallet provider as they won't get shut down soon. Even if they will.. They will issue a notice before some time so you can transfer your bitcoins to some other address.
This is the reason you would want a private key in safety deposit box or such. With a cold storage like paper you actually can use that private with many different wallets once you need it. But it can be kept offline until you need it.
The private key is important though, as it keeps it were you retain ownership of the BTC address and can use it in multiple wallets if need was there. Also security of this private key is truly essential. As with it your BTC can be taken so you really need secure storage of it.