The second time I try to open and close the "php://stderr" file descriptor, PHP begins to fail. It doesn't occur with standar files.

You can test the error with the script:
#!/usr/bin/php -q
<?php
function myerror ($error){
	if (!$errfd = @fopen("php://stderr", "w+")){
		echo "Can not open\n";
		return;
	}
	fwrite ($errfd, $error);
	fclose ($errfd);
	return;
}

for ($i=0; $i<=3; $i++){
	myerror("this is error num: $i\n");
}
?>

The output:
this is error num: 0
Can not open
Can not open
Can not open

The error:
<b>Warning</b>:  fopen("php://stderr","w") - Bad file descriptor in <b>./test.php</b> on line <b>3</b><br>
<br>
<b>Warning</b>:  Supplied argument is not a valid File-Handle resource in <b>./test.php</b> on line <b>4</b><br>
<br>