I’m having trouble sending andreceiving e-mail to a client. Sometimes e-mail comes through; sometimes it doesn’t. Sometimes it goes through; sometimes it doesn’t.
The most likely cause of the response kicked back by the server — “format of the recipient’s e-mail address isn’t valid” — is that one of the email addresses in the to, from, cc, or bcc fields is in fact screwed up. “But they look good to me,” you reply. And they might to the eye, but perhaps not to the computers, because some funny and invisible character(s) have snuck into the address.
The fix takes just a little time: Go through your address book(s), as well as the lists of previous recipients that your mail software keeps (Apple Mail > Window > Previous Recipients), and delete any instance of one of the possible addresses. Then manually retype into an email, making sure it doesn’t autofill — as that would indicate you missed a spot — and try to send.
Start with your main correspondent’s address, and test. Then repeat the process for other messagees. You may have to include your own address in the hunt. (There’s an off-chance this entails the extra step of going into Mail > Preferences > Accounts and reëntering your email address, although that’s typically only necessary when you can’t send email to ANYBODY.)
The only other cause I can guess is that somebody’s email software is screwed up, but that should only yield one-way problems, and you said the issue is bi-directional? If you can send to anybody else in that same organization, then the issue is not that their server thinks your domain or your IP is smelly.