Here are some rambling thoughts. Comments are welcome.
A traditional formulation of the problem of evil is to ask: "Why do bad things happen to good people and good things to bad people?" An interesting feature of our discourse--both academic and popular--about the problem of evil is that the second part is not much talked about these days.
There are, of course, good reasons for me not to be too deeply worried about the second part. Sinner that I am, I had better hope that good things happen to bad people. God's mercy is sovereign, and he has the right to refrain from, or at least delay, punishing the sinner. And, anyway, in the end, vengeance is his, and he will repay the unrepentant (may his grace give us the gift of final perseverance).
Still, the second part of the question does seem to embody a genuine concern for justice. Whether or not there is something bad about someone bad flourishing, there is something prima facie bad about someone bad flourishing because of her bad deeds, and yet we do observe apparent cases of this.
One interesting thing is that this bipartite formulation of the problem of evil makes it clear that this problem is one of divine justice. But considered as a problem of justice, we can see that some of what we say about the second part of the question can also be applied to the first. It is not contrary to justice to delay punishment. Likewise, it is not contrary to justice to delay reward--in fact, it might not be contrary to justice to omit reward completely (if there were a duty to reward good people, altruism would be harder).
Of course, one might hold that besides the question of divine justice, there is the question of divine benevolence. My feeling is that traditionally when religious people have worried about the problem of evil, they have worried not so much about divine infinite benevolence but about divine justice. I wonder if there is a good reason for this. Perhaps the idea is that divine infinite benevolence is sufficiently covered by God's giving us being ex nihilo, or maybe even by the infinite benevolence involved in the Father's generating the Son and the Father and Son producing the Holy Spirit. Maybe there is something right about seeing the problem of evil as a problem about justice.