To remove the re-sizable functionality of a text area use the theme_textarea() function. We will override it in our template.php:

To disable the re-sizable on all text areas use this function in the template.php file located in your theme directory.

/**
Removes re-sizable functionality on all text areas
**/
function phptemplate_textarea($element){
  $element['#resizable'] = false ;
  return theme_textarea($element);
}

The following function will remove the re-sizable functionality for one specific form, in which case we would do as follows:

/**
Removes re-sizable functionality on a single text areas
**/
function phptemplate_textarea($element){
  // if the title of our element is the one we want, then disable re-sizable
  if ($element['#title'] == 'Message'){
	  $element['#resizable'] = false ;
	} 

  $output = theme_textarea($element);
  // Uncomment the line below to see what the title of the form element you want to override is
  //$output .= print_r($element);
  return $output;
}

To find out the element name use print_r($element). The title of the element can be found using print_r($element). A cleaner easier to read approach is to utilizing the devel module.

In this example we use 'Message' as the title of the element. The resulting code is:
textarea [#title] => Message

Look for something similar when you use print_r($element)