Child-style.css no longer has precedence

I began with Blogs-MU 1.2.6. I've made a number of customizations in my child-style.css file in the child theme. Now that I've updated the parent, I see a number of those changes overridden. The culprit seems to be the way base.css is being called.

I've included 2 screen shots displaying the issue. In #1, in my child-style.css I copied the style from base.css and edited it. You can't see the whole file name but base.css?ver=1.3.1 (line 847) has precedence over child-style.css (line 258). The second example shows the only way I know of to override this behavior. I added !important to the end of child-style.css (line 313) to take precedence over base.css?ver=1.3.1 (line 14). I don't want to put !important at the end of every line in child-style.css. Besides, that won't work when base.css has !important already.

So is there something that I need to change in the way or the order that style.css gets called in BlogsMU? It's called on line 45 in the header.php which I would think would be last. Here's the command:
<link rel=&quot;stylesheet&quot; href=&quot;<?php bloginfo('stylesheet_url'); ?>&quot; type=&quot;text/css&quot; media=&quot;screen&quot; />

So what am I missing?