Category template not working with pretty permalinks

I’m working on a theme and using categories to organize pages on the site, so I have multiple category-x.php files.

The proper category template loads with default permalinks (?cat=3), but if I switch to the Numeric form (for example), category links simply load index.php instead of the respective category template.

Is this a problem with mod_rewrite? I’ve been fiddling with my .htaccess file for hours and haven’t had any success.