Failure to lock on IOS 9.3
You might try to hold home and lock buttons for a while until the device reboots the OS. This startup will require a little longer because it will be deeper than normal restart.

iOS 9.3 has brought many bugs, this should be one of them. I believe for now you should lock it with code time set to "immediately" (for safety reasons), make a YouTube video to explain the issue (I did a similar thing for a buggy update of PlayStation Vita, and it got fixed), report it to Apple and wait for 9.3.1 to come out.