Harlan,
As you've determined, the problem is with the member's email service provider.? They are blocking the emails.? Sending a bounce probe will fail until the problem is resolved (analogous to "can you hear me now??").
There is a good discussion of handling bounces here ->?
/g/GroupManagersForum/wiki/Help-Mock-up#Bounce-HandlingBest place to look is the member page -> Email Delivery History which will have a record of recent bounces including the error message(s) returned by the mail service provider - that's what needs to be sent to the tech support people.
Thanks
Toby