So this is happening on the whole site to everyone? Check the Forum Permissions, not just the usergroup permissions. Or, check and make sure the time limit for editing is long enough for users to edit posts.
Also, try disabling your modifications/plugins and see if you still have this problem.
Note: To temporarily disable the plugin system, edit config.php and add this line right under <?php
PHP Code:
define('DISABLE_HOOKS', true);