Email not being delivered to some users

I've got a closed networking site on D7 with a group of about 500 users. There are daily email updates that go out to nearly all of the users via email from our main site admin account. Most users are getting the emails but for some strange reason, a handful of users (some on Gmail accounts and some on their own domain accounts) aren't getting the emails. We've checked with the users and the emails aren't going to their spam folder, and adding our email address to their contacts hasn't helped.

We first noticed the issue when some users weren't getting the signup info email, and so we had to walk them through signing up manually. And now those same users aren't getting any site emails at all, so it's not a module-specific problem.

I'm stumped—any ideas what could be going on here? The emails are getting through to the vast majority of Gmail users, for instance, so it doesn't seem like our IP has been flagged as spam, but to be honest I don't know a lot of the intricacies and a Google search hasn't turned up much.

Thanks so much in advance!