Okay, I just tested this with the following testsplit.epub (see attached), and Sigil properly handles split at markers with no error messages and properly groks and updates naked fragments..
So the test case presented to us is somehow suspect. In fact the presence of a unclosed br tag in the test case and li tags not inside an ol lead me to believe that the structure of the original html file was quite broken (or was broken when extracted) but still an unclosed br is not valid xhtml.
Normally before running split on such a xhtml file, you should make sure you have actual xhtml code (for example br is a self-closing tag and needs to be closed in xhtml) and that it passes is actually parseable. Spliting unparseable broken code is not in anyone's best interest.
My guess is the actual case had an undeclared fragment, and Sigil did what it was supposed to and warned about it.
Code:
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title></title>
</head>
<body>
<p><a href="#editorial">From The Chief Editor's Desk</a></p>
<ol>
<li><a href="#page01">Casual Python, Part 1</a></li>
<li><a href="#page02">PCLinuxOS Recipe Corner: Slow Cooker Asian Beef</a></li>
<li><a href="#page03">ms_meme's Nook: Daddy Boot Up That Sixty-Four Bar</a></li>
<li><a href="#page04">Short Topix: Assaults On Privacy Continue Unchecked</a></li>
<li><a href="#page05">Inkscape Tutorial: Some Useful And Fun Extensions</a></li>
<li><a href="#page06">Configuring CUPS-PDF</a></li>
<li><a href="#page07">A Guided Tour Of The Data Facebook Uses To Target Ads</a></li>
<li><a href="#page08">Alternatives To Dropbox, Part 3</a></li>
<li><a href="#page09">PCLinuxOS Family Member Spotlight: masinick</a></li>
<li><a href="#page10">One Way To Duplicate Your Installation On Another Computer</a></li>
<li><a href="#page11">ms_meme's Nook: Swinging PCLOS Blues</a></li>
<li><a href="#page12">PCLinuxOS Bonus Recipe Corner: Italian Sausage With Tomatoes And Penne</a></li>
<li><a href="#page13">Configuring Late Model Epson Printers</a></li>
<li><a href="#page14">Victory! Illinois Supreme Court Protects Biometric Privacy</a></li>
<li><a href="#page15">PCLinuxOS Puzzled Partitions</a></li>
<li><a href="#page16">Screenshot Showcase</a></li>
</ol>
<hr class="sigil_split_marker"/>
<!-- editorial -->
<a id="editorial"></a>
<h3>From The Chief Editor's Desk</h3>
<p id="page01">Page 01 </p>
<p id="page02">Page 02 </p>
<p id="page03">Page 03 </p>
<p id="page04">Page 04 </p>
<p id="page05">Page 05 </p>
<p id="page06">Page 06 </p>
<p id="page07">Page 07 </p>
<p id="page08">Page 08 </p>
<p id="page09">Page 09 </p>
<p id="page10">Page 10 </p>
<p id="page11">Page 11 </p>
<p id="page12">Page 12 </p>
<p id="page13">Page 13 </p>
<p id="page14">Page 14 </p>
<p id="page15">Page 15 </p>
<p id="page16">Page 16 </p>
</body>
</html>