Spam Free WordPress is a simple plugin that inserts an HTML password form field into the comment form, and then uses PHP on the backend to authenticate the password with the one in the database for each post, so it should work without any conflicts with any other plugins.
I do see a lot of issues with this blog that should be looked into. For example, there are a lot of plugins running that could be causing a lot of conflicting problems making it difficult to troubleshoot a simple issue like a password field not showing up.
WordPress 3.3.1 runs jQuery 1.7.1 by default, but the blog is also loading jQuery 1.6.2 before it loads 1.7.1, and it loads both at the same time.
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.6.2/jquery.min.js"></script>
<script type='text/javascript' src='https://www.paulaohara.com/blog/wp-includes/js/jquery/jquery.js?ver=1.7.1'></script>
It appears jQuery 1.7.1 is loading with the Nextgen Gallery plugin.
The blog Theme is also loading its own jQuery 1.2.6, which makes 3 versions of jQuery running on the same page at the same time.
<script type="text/javascript" src="https://www.paulaohara.com/blog/wp-content/themes/PaulaO/js/jquery.js"></script>
jQuery 1.7.1 comes with WordPress 3.3.1, and should be the only version running.
There is also the WP Spamfree plugin running, which could also cause problems.
It appears there may be many issues with this blog that need to be sorted out. A good place to start is to make sure only one version of jQuery is loading, disable all other plugins except Spam Free WordPress, and see if the password field appears as it should.
The only suggestion other than not using other comment spam plugins with Spam Free WordPress, and fixing any other issues that existed before Spam Free WordPress was used, would be to also try this comments.php code:
https://pastebin.com/a35F978M