What is the perfect word/idiom/phrase for a situation when enforcement of a system is futile?

My friend usually calls this exercise in futility.

The only idiom that comes to mind is

Sisyphean task
(Greek legend) a king in ancient Greece who offended Zeus and whose punishment was to roll a huge boulder to the top of a steep hill; each time the boulder neared the top it rolled back down and Sisyphus was forced to start again

Which is quite similar as it implies futility but also necessity to start the task over.

I would say

Fight a losing battle

- to try hard to do something when there is no chance that you will succeed

source: http://idioms.thefreedictionary.com/fight+a+losing+battle

"You have won the battle but lost the war" is the expression that comes to mind for your scenerio. There is a small victory (by enforcing attendance) but then the war is ultimately lost by having students drop out entirely rather than complying with the new rule, despite its benefits.

Not to put the preservation of Boston’s “sacred sky line” on the same level as the enforcement of food hygiene (or vice versa), but the single-word adjective “quixotic” might describe these types of pursuits, especially when combined with the notion of a “lost cause”: “a quixotic lost cause” (Line 7).

In a sentence perhaps you could say that it’s “a quixotic pursuit of a[nother] lost cause.”

If "quixotic" makes the goal/pursuit seem too romantic or far-fetched, perhaps "noble" would work better: "The noble pursuit of a lost cause."