Right, mysh -- I think that's what I did.
I added the prefix zen_ to line 227 in admin/includes/classes/products_with_attributes_stock.php

using code recommended by kuroi:
$sql = "UPDATE " . TABLE_PRODUCTS_WITH_ATTRIBUTES_STOCK . " SET quantity = '$value' WHERE stock_id =$id LIMIT 1";

and that resolved the error.
My SBA seems to be working now, at least as far as being able to use the "save" button and update multiple quantities at once.

NEW QUESTION: Does anyone also use Zen Lightbox with SBA Ajax version? I'm having an issue now where my lightbox popups are showing up blank! I do not know whether this is a related issue or something I failed to notice was broken before today.