Why the TextBox’s MaxLength property set to a positive number doesn’t work
when the TextMode property is set to Multiline? What can I do to get both
properties work?

You probably have to manage this using a JavaScript function that is
triggered onKeyPress.  Something like this:

<script type="text/javascript">
    function CheckBoxLength(maxLen)
    {
        var txtBox = window.event.srcElement;

        if (txtBox.value.length > maxLen)
        {
            alert("MaxLength has reached");
            event.returnValue=false;
            event.cancelBubble = true;
        }
    }
</script>

<asp:TextBox ID="txtMultiLine" Runat="server" TextMode="MultiLine"
Width="400px" Rows="5" onkeypress="CheckBoxLength(80)"></asp:TextBox>
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For completness this is because a multiline textbox is rendered as a
textarea tag. This HTML tag doesn't have this attribute.

This is likely usually tested client side (see the other response).

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