How do I set a database back to 'Restoring...'?
It's not quite as simple as re-enabling log shipping as you need to do some initial setup to be able to switch from one instance to another. 

This article helps with that

You also need to perform some clean-up before switching back to the original primary as it will be holding databases that are now out-of-date.

If your hardware on the primary and secondary are the same and there is no performance loss or maintenance headache in staying on the secondary server then I would recommend doing that until the next failure as the step of failing back is not needed.