PHP not processing XSLT / “connection timed out” although local XSLT file

I am using PHP´s built-in functionality to transform a XML-string/dataset I receive from an external source to convert it into HTML.

While this worked fine on my development server, it doesn´t work on the live server (from another company).

I couldn´t find the problem, so they sent me some lines from the error logs:

[Tue Apr 12 15:29:33 2016] [error] [client xx.xxx.xxx.xx] PHP Warning: DOMDocument::load(http://mysite/wp-content/themes/mytheme/xsl/content.xsl) [domdocument.load]: failed to open stream: Connection timed out in /var/www/html/mysite/wp-content/themes/mytheme/functions.php on line 492

[Tue Apr 12 15:29:33 2016] [error] [client xx.xxx.xxx.xx] PHP Warning: DOMDocument::load() [domdocument.load]: I/O warning : failed to load external entity “http://mysite/wp-content/themes/mytheme/xsl/content.xsl” in /var/www/html/mysite/wp-content/themes/mytheme/functions.php on line 492

[Tue Apr 12 15:29:33 2016] [error] [client xx.xxx.xxx.xx] PHP Warning: XSLTProcessor::importStylesheet() [xsltprocessor.importstylesheet]: compilation error in /var/www/html/mysite/wp-content/themes/mytheme/functions.php on line 498

[Tue Apr 12 15:29:33 2016] [error] [client xx.xxx.xxx.xx] PHP Warning: XSLTProcessor::importStylesheet() [xsltprocessor.importstylesheet]: xsltParseStylesheetProcess : empty stylesheet in /var/www/html/mysite/wp-content/themes/mytheme/functions.php on line 498

This looks like the xslt file could not be found but that makes little sense to me, as it´s placed in a local folder, so no reason to drop a “connection timed out”?!?

This is the function which creates the errors, looks pretty fine to me.

// Execute XSLT on given string
function xslt_transformation($the_xml_string)
{
    $xml = new DOMDocument;
    $xml->loadXML($the_xml_string);

    $xsl = new DOMDocument;
    $xsl->load('wp-content/themes/mytheme/xsl/content.xsl');

    $proc = new XSLTProcessor;
    $proc->importStyleSheet($xsl);

    return $proc->transformToXML($xml);
}

Any hints or ideas what I could look for?

Update 1: Meanwhile I altered my code, to make sure it looks for a local file for the XSL. This might save a http-call to a file that lies just a subdirectory away. At least I hope so, I don´t know if PHP is smart enough to check that before.

Update 2: I did some testing with the locally loaded XSLT and the whole system seems to run much faster now, at least I got no dubious timeouts this time. I´ll make some more tests with larger XML documents.