Mail compatibility issues have been very common with wordpress users, specially at the time when they are working with WooCommerce integration in their website. By the way there are different reasons when you figure out mail send issues. First step to solve the problem is to find the root cause, and for it you need to check and find out which problem is in which mail. Problem might be in
When new orders are pending or Transactional emails are accidentally disabled
Main problems with the mail sending issue:
1-Problem in deliverability-
To check deliverability install & activate wp mail logging
Generate test order, and check whether emails are generated by the order or not.
2- Spam issues
To check the spamming nature of mail, you can use tools like email on acid, litmus,etc.
Once you find the spam issue, you can go ahead to find out the ways to resolve the issue. For immediate answers you can connect with wordpress support team
3- Reputaion-
To check the reputation of your mail you can use tools like email on acid, and sender score etc.
To fix email reputation, you should remove bounced emails from general email list, so that it cant harm email lists,