Hi Ilya,
This is happening because we are using regular WPF Buttons in those locations and Microsoft's ButtonBase.OnLostMouseCapture code will blur focus (move it back to the main focus scope) when in a toolbar/ribbon. That in turn causes the popup to close.
We are going to work around it by adding some custom primitive button classes for use in the MonthCalendar that will prevent that focus blur. Those updates will be in the next maintenance release (build 651).