Just realised that some of the animated GIFs do not contain GCE (graphic control extension). Here is the refactored is_ani() function:

<?php
/**
 * Detects animated GIF from given file pointer resource or filename.
 *
 * @param resource|string $file File pointer resource or filename
 * @return bool
 */
function is_animated_gif($file)
{
    $fp = null;

    if (is_string($file)) {
        $fp = fopen($file, "rb");
    } else {
        $fp = $file;

        /* Make sure that we are at the beginning of the file */
        fseek($fp, 0);
    }

    if (fread($fp, 3) !== "GIF") {
        fclose($fp);

        return false;
    }

    $frames = 0;

    while (!feof($fp) && $frames < 2) {
        if (fread($fp, 1) === "\x00") {
            /* Some of the animated GIFs do not contain graphic control extension (starts with 21 f9) */
            if (fread($fp, 1) === "\x21" || fread($fp, 2) === "\x21\xf9") {
                $frames++;
            }
        }
    }

    fclose($fp);

    return $frames > 1;
}