Are there any space or sending limitations imposed by Zendesk?
No, there are no space or sending limitations for email notifications sent from tickets. The exception to this is the 1,500 number a day limit for Gmail Connector. For more information on the Gmail Connector limit, please see What does "You've reached your Google sending limit" mean?.
Alternatively, if you receive an email stating that a storage upgrade is required or you are running out of space, it is either due to your email provider limitations or spam. We recommend reaching out to your email administrator or provider for confirmation.