Feedback box – should it close automatically after the comment is sent?

I am designing a feedback box and I want to implement some sort of "Don't bother me anymore" action that will close the box indefinitely for the users that don't want to give feedback or don't want to see the box/button "ever again".

The question is: Should I close the window automatically permanently after the feedback or should I leave it so the user can access it anytime?

The client suggested that it could close after the feedback is sent, but then again, you would like the users to have the opportunity to easily access a form to give more feedback if they wish to do so. I think that maybe leaving it there is not such a bad idea, as users can also close it "forever" anyway after they give feedback with a click (the "Don't bother me anymore").

Does either approach have more (dis)advantages and why?