I was now able to reproduce the issues using our File Transfer sample. However, this behavior might be related to this Cordova issue. We've had a few reports also indicating that it is intermittently appearing in certain cases causing the window.requestFileSystem() callbacks not to fire. We are not aware of a workaround but we're monitoring the progress of the task and as soon as Cordova applies a stable fix, we will make sure to take it as well.
If you want to test whether the callbacks are properly invoked in your app, you can try debugging the app while running it on a device. If the callbacks are fired, but the file is still not downloaded, you should be able to get an error indicating the cause for the issue.