While it can't be discarded 100%, based on your description the problems are most likely not directly related to Limesurvey.
Most respondents do not have these problems, the issues are with specific domains. So the setup in Limesurvey and the SMTP server seem to work.
Sending mass emails is a science in itself. Trouble shooting is not easy, especially when the problem is with the receiving mail servers, as it seems, as this is no general issue, but an issue with specific mail servers on the receiving end.
Most likely the server on the respondents end is considering your emails spam, which can have a variety of reasons:
- Email text and subject contains potentially "suspicious" keywords that trigger spam filters
- The IP of the SMTP server used to send the emails is on a black list, the server is in a "bad neighborhood", or from a provider that is known for a high ¨% of spam activity, etc.
- SMTP server that is not correctly configured. Today, many receiving mail servers refuse to receive emails from servers that do not follow the rules of best practice on how to configure an email server
- Too many wrong email addresses in the database for this email. Email providers often consider a source as suspicious when the send emails to a lot of non existing email accounts for their domain.
- etc.
Did you configure a bounce email? Some email servers "respond" with the reason, when they block emails to be delivered.
What is the SMTP server you are using? Something like Sendgrid? Or is it hosted by your organisation?
All in all, given that the system generally seems to send emails (many respondents seem to receive the emails just fine) I think we can ignore the configuration in LS or the configuration of the SMTP account. I think you will need to look into the configuration of the server, the neighborhood of the server, potential spam filters on the receiving end, etc.