You should try to run smtp4dev on the machine your SiteFinity project is hosted on.
Configure the port in smtp4dev to 26 (must be a free port).
Then go to your SiteFinity project to Administration > Settings > Advanced > Notifications > Profiles > your_profile
Over here, set host = localhost and port = 26.
When you now run an issue in your email campaign, the mails will be sent to smtp4dev tool and all successful sent mails will appear in this tool.
Verify in this tool if there are emails missing. If all emails are there, SiteFinity has successfully sent out the email campaign and this will be most likely an issue on the mailserver.
You might need get IT involved to further investigate this.
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and vote to affect the priority of the items