This problem can also occur if you hide and then show again the modal window too rapidly. This was mentioned elsewhere for question, but I'll provide some more detail below.
The problem has to do with timing, and the fade transition. If you show a modal before the fade out transition for the previous modal is complete, you'll see this persistent backdrop problem (the modal backdrop will stay on the screen, in your way). Bootstrap explicitly does not support multiple simultaneous modals, but this seems to be a problem even if the modal you're hiding and the modal you're showing are the same.
If this is the correct reason for your problem, here are some options for mitigating the issue. Option #1 is a quick and easy test to determine if the fade transition timing is indeed the cause of your problem.
Here are some related bootstrap issue tracker posts. It is possible that there are more tracker posts than I've listed below.