Zazu did do a much better job watching Simba and Nala, even if he did lose them. Timon and Pumbaa lost Kiara after what...Three minutes? They didn't even make it to a musical number xD
As to why Simba kept asking them to watch his daughter? Most likely because they practically raised him, and that's got to be worth something. They kept him safe and got him to adulthood. Seems as though if they could just stop arguing with one another, they could have done a better job with Kiara. Then again, how would the story have progressed if they hadn't kept losing her? xD
As a random thought...Anyone think that Simba may hold a slight grudge against Zazu? Nothing strong, just asking out of humor. He could have remembered how "horrible" of babysitter Zazu was. Or the simple fact that him and Nala outsmarted him so easily.