Looks like we can't reproduce the issue or there's a problem in the test case provided.
Can see datePicker component, it's covered by soft keyboard.
android 4.1 build-in browser
1. Set the focus on a form textbox, system will show the soft keyboard.
2. Click the datepickerfield component.
Soft keyboard should be closed, and pop-up a datePicker bar on the bottom.
Soft keyboard NOT be closed, and can not see the datePicker bar that is under the soft keyboard.