The Sprinkler still has a "Turn On" option when it is completely depleted of fuel. If clicked, it turns on and runs indefinitely without the need to fuel it ever.
Steps to Reproduce
Start a new game, no mods, default everything. Craft and place a sprinkler then turn it on and let it run out of fuel. It then turns off and can be turned on once again which will then cause it to run forever without refueling being necessary.
This issue has not been confirmed by a developer yet.