The slang term ' junkie' is someone addicted to, whatever is. Someone who keeps going in the feeding of a self-destructive habit, in spite of severe setbacks, is an 'addict'. (Perhaps literally a gambler: a gambler regards losses to be temporary setbacks on his or her way to regaining a lucky streak, and keeps on gambling.) Someone who goes irrationally in the face of setbacks is a 'fool', or 'gambler'. Those who are fighters, steadfast, and so on (any admirable names for those who display courage, persistence and fortitude), keep going despite setbacks that would stop most people, but do not keep going in the face of all possible setbacks. Of course, everyone keeps going despite some setbacks.

I think the other answers deal with normal individuals who do have some upper bound on their perseverance, and therefore do not keep going despite setbacks, only despite some setbacks. (Someone who persists in the face of any and all possible setbacks *including* his death is a fictional figure such as a zombie or ghost.) Someone who persists in the face of any and all possible setbacks (short of the cessation of his life) is a plain 'madman'. It doesn't match your required definition strictly, but carries a certain romantic flair that pretty much suggests what you required. Words like “la reata” in Spanish became “lariat” and desparado became desperado. When the Americans immigrated into the area they modified the language of the region to suite. The term became associated with “scofflaws”, people that openly disrespect the law. According to their oral history, the term desparado, described travelers that did not want to pay a toll and circled, off the road, around the military posts. And as above “desparado” is a person that was not stopped. The soldiers would stop the travelers and demand the toll be paid for them to continue on. Spanish law levied a toll to travelers on the Camino Real in order to pay for these soldiers. As such the road is protected by garrisons at intervals along the road. Camino Real literally means “Royal Road”. Spain created the Camino Real from Mexico to Santa Fe, New Mexico, in 1598.

Now that I know your restrictions, I think I have the right word.

Persistent aim definition