I added the following to make the popup disappear on its own, otherwise it wont go away unless you click a different date from the currently selected one. I did it on mouse leave because it felt more natural.
in the initializ method:
this._popUp.MouseLeave += new MouseEventHandler(_popUp_MouseLeave);
then the method:
void _popUp_MouseLeave(object sender, MouseEventArgs e)
this._popUp.IsOpen = false;