Missing order emails are among the most damaging faults a shop can have, because neither you nor the customer knows an order has happened. Work through this in order.
1. Is WooCommerce trying to send them?
In WooCommerce settings, check the Emails tab. Confirm the notification is enabled, and that the recipient address for admin notifications is correct – it is easy to leave it as an address nobody reads.
2. Are they being sent but filtered?
Check the spam folder first. Then check the sending address: mail sent "from" a customer's own address will fail authentication and is very likely to be filtered or rejected. Send from your own domain and use Reply-To for the customer.
3. Fix the sending method
WordPress's default mail function authenticates poorly. Use an SMTP plugin sending through a real mailbox on your domain – see WordPress cannot send email. On a shop this is not optional; order confirmations that land in spam cost you money and generate support calls.
4. Check the background queue
WooCommerce sends some emails through its scheduled task system rather than immediately. If that queue is stalled, emails simply never go. See Action Scheduler: why background jobs stop running. This is a common cause and it is invisible unless you look.
5. Prove it end to end
Place a real test order and watch what happens. A test email from a plugin only proves the mail path; it does not prove WooCommerce is triggering the notification.
Keep a record
A mail logging plugin records every message the site attempts to send. When a customer says they received nothing, that log answers in seconds whether it was sent, and is worth having in place before you need it.