email delivery problem

My medical provider has an interface that mediates between provider and client. It is, as you might immagine, behind a firewall. When a provider sends a message to a client, the system sends a "You have mail" email to the client, using regular email protocols.

My issue is that much of the time the email that they are supposed to send does not appear in my HughesNet mailbox.

Wonderful opportunity for finger pointing?

In response to my request for a log, this is what I received:

You can let your email provider know that our email notifications are sent from the following email address: MYCHART.SUPPORT@UCDMC.UCDAVIS.EDU The SMTP response codes for the emails sent to your email address indicate that the messages are being successfully delivered from our system to their recipient email server. The most recent email message sent to you was on 10/22/20 at 5:25 pm Pacific time.

Is it possible to use this data to determine what might have happened? FWIW, I clear my mailbox hourly and delete messages once they are downloaded. The referenced email is not in my trash folder.