This question has a very broad answer. As it depends upon your implementation of both hardware and software.
In very short -
That all depends on your code. The hardware should be able to be left on indefinitely, assuming it is all within spec's. Assuming that, then the biggest concern is the code running on it. Where largest problem of concern is running out of resources. Such as memory. If your code as a memory leak then it will be a problem. Or if there is a bug in the code that can cause it to get stuck. The later can be addressed by employing the WatchDog, which will reset (loose all data) if the code gets unexpectedly stuck.