This is a good question.
I believe that yes, we should still help people knowing full well it will bite us in the ass. I have a seven time policy with people I know. After 7 times of giving and receiving nothing in return, I sever ties. Those people cannot be helped.
I had a friend once who was constantly in trouble with the law. I'd bail his ass out of jail. He was borderline homeless and his friend circle was fading fast after high school. I took it upon myself to come help him when he'd call every 8 months or so. Buy him lunch, loan him money, drive him places he needed to be (see: court).
All I got in return was drunk dialings, idiotic behavior while driving him around (see: breaking my window button on the passenger side after telling him numerous times not to hit the fucking button so hard. Eating red liqourice (fuck spelling) and then spitting out of my car window, leaving red hardened streaks on my door that stripped the pain off when trying to clean. Him asking me to pull over because he had to pee so bad, only to have him come running back to the truck, throw open the back door, and toss in a webber grill or a christmas outdoor nativity set, then hopping in and yelling "drive drive drive!" as well as countless other things).
I realized one day that this person was beyond help. I haven't taken a call from him since.
However, with that in mind, I believe that we must continue to be good people, if only for the sake of knowing that you're better than other people. If you can't get that fuzzy feeling from helping someone, get it from knowing you're better than them. Period.
If everyone just gave up today. If everyone just stopped trying, we'd be so much worse off. Shit is bad now... imagine if everyone just said "fuck it."
Take a deep breath and know that while this crazy bitch is a lost cause, you will one day help someone who will return the favor, and hopefully then some.
I have a lot of "and then some" friends now.
If anything, this is a great way to see who your true friends are. It helped me weed out the useless ones. As someone who hates everyone and who enjoys their alone time, it was important to get a list of people I'd feel fulfilled with hanging out with.
Not people that go "hey, are you thirsty? Yeah? Cool, grab me a coke while you're up."