Changes from comments.

- Move private instance variable.
- Reset errorMessage.
- See https://github.com/Seldaek/monolog/pull/248

src/Monolog/Handler/StreamHandler.php

@@ -24,6 +24,7 @@ class StreamHandler extends AbstractProcessingHandler
 {
     protected $stream;
     protected $url;
+    private $errorMessage;
 
     /**
      * @param string  $stream
@@ -60,6 +61,7 @@ class StreamHandler extends AbstractProcessingHandler
             if (!$this->url) {
                 throw new \LogicException('Missing stream url, the stream can not be opened. This may be caused by a premature call to close().');
             }
+            $errorMessage = null;
             set_error_handler(array($this, 'customErrorHandler'));
             $this->stream = fopen($this->url, 'a');
             restore_error_handler();
@@ -71,7 +73,6 @@ class StreamHandler extends AbstractProcessingHandler
         fwrite($this->stream, (string) $record['formatted']);
     }
 
-    private $errorMessage = null;
     protected function customErrorHandler($code, $msg) {
         $this->errorMessage = preg_replace('{^fopen\(.*?\): }', '', $msg);
     }