Mmm. Then we don't have more clues to move forward.
What I can recommend is to add the code:
if(!empty($order->order_status) && $order->order_status=='ready')
hikashop_writeToLog(debug_backtrace(DEBUG_BACKTRACE_IGNORE_ARGS));
before the line:
$order->order_id = parent::save($order);
in the file administrator/components/com_hikashop/classes/order.php
This way, each time the status of an order is updated to "ready" via HikaShop's API, the data of situation will be logged in the "payment log file" of HikaShop (it is available in the "Files" section of the HikaShop configuration).
And next time you have the issue, please provide the payment log file content so that we can check the situation. This should allow us to better understand what is causing the problem, supposing that the MySQL query log provided by the hosting support really corresponds to the issue.