Hi Steve,
WooCommerce, and most plugins sending email, send mail by using the wp_mail() function that is a core function of WordPress. So it does seem strange that you are getting some alerts but not others.
Here’s what you can try:
1. Check for Pending Orders
Your orders are perhaps pending. Pending orders are orders where the customer clicked “Place Order” but abandoned the payment page (depending on the payment gateway, i.e., PayPal) or had their credit card transaction declined. If you have pending orders, these orders will not generate emails.
If you have pending orders but receive payment for them via a payment gateway such as PayPal, which requires a notice to update order status on your site. In this case, you are not looking at a email issue; you are looking at an issue with your payment gateway and may need to submit a support ticket to the Woo Team
2. Check your Email Settings
Orders that are properly updating to Processing should generate an email. Another possible issue is having mistakenly disabled (maybe not intentionally) emails from sending. Double-check that “Enable this email notification” is ticked for order notifications. An additional test should be setting the Email Type to Multipart.
If you are sure your other emails are being generated then the above is the best place to start checking things.
Let us know what you find,
Jason