Clara.io autosaves, you don't have to explicitly save your project. You can do an export if you want to have a local copy.
Or are you saying that clara.io is giving you a big scary warning on the bottom of the screen saying that your changes aren't saving? That's usually a network connectivity issue. Clara.io keeps trying to connect, so if your network resolves, that warning should go away.
One way of verifying that changes are being saved is to open your scene in another browser tab. If you make a change in one tab it should mirror on to another tab.