There is no way for the user to opt out of receiving ticket emails, but I found this when looking at the email templates:
Auto-Responder Warning; Subject - Warning: Confirmation emails turned off
When would this be sent to the user?
When a user sends a lot of email messages in a short time, it usually indicates that there is a feedback loop where the user's account is sending an automatic response, Deskpro is sending an auto-reply, which triggers another automatic response, and so on.
In this situation, Deskpro will automatically disable ticket notifications to the user. A final email is sent to inform the user what has happened, which will include this phrase.
If you wish to reenable auto-replies for the user, look at the drop down list on the right hand side of the users profile.