When Service Desk can't send email notifications, the non-sent emails will be stored in install-folder\site\mail_undeliverable folder. Anyway Service Desk administrator can force the app to resend those emails?
CA Service Desk 17.3 and higher versions
You can move 50 (oldest) files in mail_undeliverable to mail_queue folder. Then move another 50 files like 10 minutes later and continue until all files are moved. And if the mail_undeliverable folder is emptied and those files don't come back, the stuck emails are sent; if some comes back to this mail_undeliverable again, then you would need to investigate why that specific email can't be sent(for example, the email address is wrong).
Why move 50 files at a time and wait? because you don't want the mail server be flooded and therefore reject sending them
This should be done on background server or primary server.
Some reasons why emails are not sent and stored in mail_undeliverable folder