How to reproduce: 
radDateTimePicker1.DateTimePickerElement.ShowTimePicker = true;
radDateTimePicker1.Format = DateTimePickerFormat.Custom;
radDateTimePicker1.DateTimePickerElement.CalendarSize = new Size(330, 250);
radDateTimePicker1.ReadOnly = true;

Workaround: 
this.radDateTimePicker1.DateTimePickerElement.ShowTimePicker = true;
this.radDateTimePicker1.Format = DateTimePickerFormat.Custom;
this.radDateTimePicker1.DateTimePickerElement.CalendarSize = new Size(330, 250);
this.radDateTimePicker1.ReadOnly = true;

RadDateTimePickerCalendar calendarBehavior = this.radDateTimePicker1.DateTimePickerElement.GetCurrentBehavior() as RadDateTimePickerCalendar;
calendarBehavior.TimePicker.TimePickerElement.ReadOnly = true;