In all likelihood, the context_id of the comment is the object it's commenting. Therefore, it will only inherit delete permissions through the object it's attached to. You probably don't want to give delete perms on the object, so you will have to edit the commenting procs to grant delete permission on the comment to whomever you wish, be it the user who created it, or to Registered Users (I don't really believe this is what you want).
Take a look at general-comments/www/comment-add-3.tcl and see the part where the permissions are added. That's what you need to fix. If you're really fancy, you can add a parameter to the general comments package so site admins can configure who gets granted the delete permissions.
