Email notifications not getting sent out to external emails when added to watchlist

[Jackie23]

Our ServiceDesk will get interactions from users outside our domain (usually their account is locked out so they send a question via Gmail). They add their email to the watchlist so they get a notification when comments are added. 

We have been seeing inconsistencies with notifications not getting delivered to the external emails. They mainly are not getting sent on the initial communication, but will possibly get the rest afterward. 

The activity feed says it has been delivered and I have looked at the outbound logs. It says emails are getting sent out, but upon testing in our external emails they never actually get sent out. 

We have customized notifications for our assignment groups, but everything is working within our domain. We also  use a user named "Nonau Affiliate" with a fake number and email in the "Requested for" for all tickets that come in this way. I have attached the user profile below. 

Has anyone had this issue before? Can anyone think of where I can look to find the source of the issue?

[SanjivMeher]

Can you check if the external emails are allowing to receive emails from ServiceNow. Sometimes you need to give permissions in the DL to allow emails from external domain. Also I would suggest you to check the email logs to see, if there are emails coming back to ServiceNow about non-delivery.