It may be useful to first consider utilitarianism as the opposite of what one is looking for. Here is Wikipedia's description:
Utilitarianism is a family of consequentialist ethical theories that promotes actions that maximize happiness and well-being for the majority of a population.1 Although different varieties of utilitarianism admit different characterizations, the basic idea behind all of them is to in some sense maximize utility, which is often defined in terms of well-being or related concepts.
If the moral goal is to "maximize utility", pursuing a futile goal would not be in line with this moral philosophy. If the only standard of right and wrong are the consequences there is no justification to pursue a futile goal especially if more achievable goals are available.
The opposite of this, and what you are probably looking for, would be divine command theory. Here is Wikipedia's description:
Divine command theory (also known as theological voluntarism) is a meta-ethical theory which proposes that an action's status as morally good is equivalent to whether it is commanded by God. The theory asserts that what is moral is determined by what God commands, and that for a person to be moral is to follow his commands.
Whether a moral good is likely futile or not is irrelevant. Even questions asking why or how one is supposed to do something are irrelevant. All that is required is a first step of obedience. God not only justifies what one is doing, but God is the main actor.
From this perspective that means the more futile the moral good the better. The miraculous action of God is made manifest by the futility of human beings achieving the moral good.
This is not easy for even religious people to make sense of. They, like anyone else, think they are the main actors when obeying divine commands and they are just as perplexed when asked to do something completely futile like crossing the Red Sea.
Here is the question:
Are there any notable works that touch on pursuing a moral good that is likely futile?
Perhaps the most notable work is the Old Testament. When reading this consider using a commentator as a guide. One commentary that does not demythologize the events is David Pawson's Unlocking the Bible. This will most clearly bring out the significance of "pursuing moral good that is likely futile" from the perspective of believers confronted with the challenges and rewards of practicing divine command theory.
Wikipedia contributors. (2019, August 6). Utilitarianism. In Wikipedia, The Free Encyclopedia. Retrieved 19:05, August 20, 2019, from https://en.wikipedia.org/w/index.php?title=Utilitarianism&oldid=909687983
Wikipedia contributors. (2019, May 13). Divine command theory. In Wikipedia, The Free Encyclopedia. Retrieved 19:06, August 20, 2019, from https://en.wikipedia.org/w/index.php?title=Divine_command_theory&oldid=896916315