This is so terribly wrong. Nobody lives off foreign aid except politicians. The average African sees virtually none of the money you send them. Not to mention that the point of foreign aid (on large scale terms) is charitable... they don't have to pay it back. I guess you could call it payback for countless years of colonialism, but it's nowhere close to a fair trade. It is not a lost cause. There's tons of organizations doing great work here. Granted, for every organization doing things well there's ten screwing it up, but it's the developed world's duty to help.
How could the thought of quitting even cross your mind? Since when was it acceptable to "give up" on a whole continent of people? What makes their lives any less worthy of being lived than yours?
On the other hand, Africa is seriously fucked up... this happened less than a week ago about an hour and a half from where I'm living...
http://www.nation.co.ke/News/-/1056/562702/-/u4b2eb/-/index.html