Part of being a good GENI citizen is releasing resources when you're not using them anymore. When you have finished all parts of your lab assignment (successfully), finished your network diagram, and retrieved all data from your remote hosts, use the "Delete" button at the bottom of the canvas in the GENI portal to delete your resources.
Once you delete your resources, you will no longer have access to them, and all the data on them will be deleted. Make sure that you have saved everything before you delete your resources.
You don't have to delete your slice; it will be deleted automatically when it expires.
In general, your resources will not persist forever if you don't delete them. Resources are reserved with an expiration date, at which time you will lose access to them.