All group members have their email settings configured to receive your messages from their groups in "real time" as the default.
First, have the person check in their spam/junk mail folder. If messages aren't there, contact the Core office to have ALA work with the person's IT department to troubleshoot the problem.
While we have run into a handful of issues where someone has changed jobs and didn't update the email address in their profile, this is fairly rare. We've also had a couple of instances where someone's email was set to undeliverable in Connect because of a bounce, but we've been able to troubleshoot those and restore email service to them. All of which is to say that it seems to be pretty rare there are technical issues with email getting delivered to your group's members.
If you haven't heard from a particular group member, the quickest way to find someone's email address is to look at your roster on the Core website, log in, and refresh the page. You must manually reload the page to see contact information for everyone on your group. You can then reach out to that person to ask if they're receiving committee emails from Connect. If they're not, contact the Core office to have ALA work with the person's IT department to troubleshoot the problem.