I found the stock app to work a couple years ago, but then after some update along the way it became unstable. I switched to a dedicated app for my email service. (Gmail app)
Have you opened and previously deleted these emails on a desktop (or laptop) computer? If they are disappearing from the phone app it's likely syncing to what is on the email server. So, when you delete from a web client your phone will show the exact same thing, and vice versa.
Are you using an email client (meaning NOT a web browser) on the desktop/laptop to access the email account? If you are it's likely the client pulls the email from the server to the local client. This would make these emails unavailable to your phone client. If you are using an email client on a PC there's usually a setting like "Keep email on server until deleted" that needs to be turned on.
Not knowing your whole setup makes it difficult to figure this out, but maybe with more info I can help.