I've been wrestling with something like this myself. I wrestle with a minor form of depression every now and then. It doesn't last long when I do have it (usually a few days), as such I have never been diagnosed as clinically depressed (apparently you need to be depressed for at least 6 weeks at one time in order to be diagnosed), but there is something Ive been wrestling with for years now.
Just three days ago I feel into this, and one night burst into to tears pleading with God to help me. Well, as much as I dont want to say it, I don't really think or feel like he did. I came out of it as I usually do (after a few days), only this time, I got very irrational about my beliefs and how God works (saying and believing things such as "everything I do is in vain. My involvement in the fight against poverty is all in vain only to make myself better, how could I be so bold to believe it was God himself leading me to that cause? Things are the way they are, everything will come to pass and we should just shut up about it and accept that. We had our chance for paradise on this earth and lost it etc). Now I dont know if it's because I am so exhausted after this experience, but while I think a part of me may know what I said is wrong, I truly believed it the last three days and I think I may have just confused myself. Nonetheless, I am sure feeling very uninterested in being involved in the charities and social justice work I was once in. I'm also very uninterested in God right now.
Why does he allow it? I dont know, like everyone has said, I guess it's just free will. I certainly dont feel as if I choose to be this way, but my condition isnt even bad enough to receive a diagnosis, so I cant really blame it on genetics. The only blame I can place is unto myself, that I somehow let myself get affected this way by certain things. Still I know that doesnt make it any less discomforting that you reached out to God and dont feel as if he answered.
What Im wondering more so now than ever though, (and again this may just be after math of how I was feeling the last three days) is why God lets things such as famine continue, when there are thousands, if not millions working toward and praying for such suffering to end? People are always saying, "God sheds his tears for earth" but why? What good is it doing anyone to shed tears for something he has the power to stop, right now if he wanted do? Really I guess the only answer is, only God knows...
Just three days ago I think I would have been able to accept that (I wasn't angered by the Tsumani, for example, ) but right now I feel as if I can't and am very distraught.