Why is the pdf at this link periodically giving a 404 error?
It is not possible to debug. We can't see the source of the website, how it is configured, etc.
There are commonly accepted reasons for 404 responses (see HTTP 404 for some examples) but a website can be configured to return 404 for any reason at all (depending on what the website author decided to do with a particular request).
There is nothing preventing the return of a 404 error because it happens to be Friday today (to give an example) or because Tim Post lost his keys.
It is entirely up the the author of the website.
As the website appears be be reasonably secure we don't have access to its configuration or source code so we have no way to find out.
What do we know about the website
It uses the following:
and a bunch of other technologies.
None of this is accessible from outside so it doesn't help to debug your issue.
Source Site report for www.moreshesashkenaz.org
Debugging with firefox
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:40.0) Gecko/20100101 Firefox/40.0
Accept-Encoding: gzip, deflate
Cookie: 4957186c87cf302cf91cc7d50c18a108=S%2CSKrRvB%2CMirDEhhz%2CPgH2; jfcookie[lang]=en
If-Modified-Since: Fri, 14 Aug 2015 11:14:25 GMT
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en-us" lang="en-us" dir="ltr">
<title>404 - Error: 404</title>
<link rel="stylesheet" href="/templates/system/css/error.css" type="text/css" />
<div id="errorboxheader">404 - Component not found</div>
<p><strong>You may not be able to visit this page because of:</strong></p>
<li>an <strong>out-of-date bookmark/favourite</strong></li>
<li>a search engine that has an <strong>out-of-date listing for this site</strong></li>
<li>a <strong>mistyped address</strong></li>
<li>you have <strong>no access</strong> to this page</li>
<li>The requested resource was not found.</li>
<li>An error has occurred while processing your request.</li>
<p><strong>Please try one of the following pages:</strong></p>
<li><a href="/index.php" title="Go to the Home Page">Home Page</a></li>
<p>If difficulties persist, please contact the System Administrator of this site.</p>
<p>Component not found</p>
Note the css included in the response:
This includes the following comment:
* CSS Document for offline page
* @version $Id: error.css 14401 2010-01-26 14:10:00Z louis $
* @package Joomla
* @copyright Copyright (C) 2005 - 2010 Open Source Matters. All rights reserved.
* @license GNU/GPL, see LICENSE.php
* Joomla! is free software and parts of it may contain or be derived from the
* GNU General Public License or other free or open source software licenses.
* See COPYRIGHT.php for copyright notices and details.
Note the following:
CSS Document for offline page
The website is including this CSS because it has been coded (for whatever reason) to return this for "offline pages".