You need to pair each textarea to it's input that presents the count of chars left.
You normally need only keyup or down, not both.
<textarea name="limitedtextarea1" onKeyUp="limitText(this,this.form.countdown1,200);">
</textarea><br>
<font size="1">(Maximum characters: 200)<br>
You have <input readonly type="text" name="countdown1" size="3" value="200"> characters left.</font>
<textarea name="limitedtextarea2" onKeyUp="limitText(this,this.form.countdown2,200);">
</textarea><br>
<font size="1">(Maximum characters: 200)<br>
You have <input readonly type="text" name="countdown2" size="3" value="200"> characters left.</font>