This has happened to me and a lot of other people. For no known reason, your iPhone will not stop asking for your Apple ID password. I have no idea what causes this, but it is extremely annoying. Sometimes a simple Shutdown and Restart of your iPhone will remedy this problem, but if that does not work then you should read this article which contains gradually escalating troubleshooting steps to fix this issue. The last few troubleshooting steps are pretty drastic, so proceed with caution.