Need confirmation: Membership scheduled reminders do not sent to any email on bounce lists?
Mail is designed to go out so long as email is not on hold. The point of the bounce thresholds is ensure the system keeps sending to an email address in cases where there is a reasonable prospect that the email will get through. And to not send when the likelihood drops too low.

Suggestions if small propotion of list not seeing email:
1. Have client check spam folder.
2. Set up SPF record for the emailing domain.
3. Reduce 'spamminess' of mailings, eg no attachments, no broken html, no words likely to be flagged. 
4. Use a mail delivery service like the Mandrill one we put out when they provided 12k free emails per month (I think minimum spend is now $35-40/month so targetted at bigger installations), or the new SparkPost integration extension.