Hi,
First thing is to check the history of these orders.
There, you should have a row with the username of the user changing the status and / or the IP address.
That should give you a first clue on what is going on.
For example, if the IP address is the one of hikashop.com then it's likely because you have the cron task configured and you have a mass action or a plugin which changes the status automatically periodically when our server triggers your cron task.
If you have nothing in the history for these order status changes, then it means that whatever is changing the order status doesn't do it through HikaShop. It could be that a custom plugin directly run a MySQL query to change the status for example. That would also explain why there is no emails sent by HikaShop.
The most likely culprit is a mass action. So I would also recommend looking in System>Mass actions for any mass action on the "order" type which is published. Bonus points if the mass action has triggers like "every day" or "every hour".
If you don't see an email for these order status changes in the Customers>Emails history menu, then HikaShop didn't send the email notifications. If you don't believe this, you can enter your email address in the "BCC" field of the "order status notification" so that you get a copy of the emails sent by HikaShop when changing the order status.