To reproduce:
- Set the AutoSelectNextPart property to true.
- Selelct the entire text and try to enter the date.

Workaround:
radTimePicker1.TimePickerElement.KeyDown += TimePickerElement_KeyDown;

void TimePickerElement_KeyDown(object sender, KeyEventArgs e)
{
    if (this.radTimePicker1.TimePickerElement.MaskedEditBox.TextBoxItem.Text.Trim('A', 'P', 'M', ' ') == this.radTimePicker1.TimePickerElement.MaskedEditBox.TextBoxItem.SelectedText.Trim('A', 'P', 'M', ' '))
    {
        ((MaskDateTimeProvider)radTimePicker1.TimePickerElement.MaskedEditBox.Provider).SelectFirstEditableItem();
        e.Handled = true;
    }
}