The reason for the DropDown portion of the DateTimePicker not getting closed when selection is made is because unlike the DatePicker/TimePicker controls there are multiple parts of the DateTime object that could be selected. When using DateTimePicker you could select a date from the calendar and select a time from the clock part of the control. In this case if the DropDown is closed after only one selection you will need to open it twice to be able to select the full date and time.
Achieving the desired behavior is easily achievable with the use of the SelectionChanged event. In that event you will need to:
Check if new items (new selection) have been added with the use of the SelectionChangedEventArgs
If the previous condition is true set the IsDropDownOpen of the RadDateTimePicker control to false.
the next code snippet shows the previous approach:
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