The control is declared as follows :
 <telerik:RadDateTimePicker InputMode="DateTimePicker"
                            IsTabStop="False"
                            Height="36"
                            Focusable="False"
                            Validation.ErrorTemplate="{x:Null}"
                            SelectionOnFocus="SelectAll"
                            x:Name="OutwardStartDate"
                            BorderThickness="2,2,2,2"
                            SelectedValue="{Binding OutwardDepartureDate, Mode=TwoWay, ValidatesOnDataErrors=true,
                                                                     NotifyOnValidationError=true}" >
I've failed to find any XAML attributes in order to auto-close this control when a date is selected. I've stumble upon this post on the official website, however the question is dated from 5 years ago and none of the current answers solved my issue.
                        
You can simply hook to the SelectionChanged event.
In your XAML as follows :
and in the code behind change the IsDropDownOpen property :