People would need to keep their computers on for this to work right? What if you need to access your data and they turned their computer off? Great idea though, I'm excited to see how this turns out.
I imagine people would have an incentive to leave their computers on 24/7 to earn more. I know I certainly will. I also imagine that file storage would have redundancy for safety reasons.
you need to leave your computer running. storj uses "heartbeats" to check the status of a node. If a node drops (ie you turn off your server), it will seek out another node to copy the file you hosted, then it will end your contract. It does this so 3 copies (minimum) of the hosted file is available online at all times. When you contract ends you will no longer be paid storj because you are no longer providing the service of hosting the encrypted files.
There's no way to resume a contract? That's a bit silly. What if I need to turn off a server for maintenance? Do I have to start a new one?