Why are we not getting any e-mails?

At my workplace, we have a shared e-mail for everyone at the store. We sign in from the g-mail main page and it’s a g-mail inbox, but the address uses our own domain name.

For the last week or so, we haven’t been getting any e-mails. I tried sending one from my personal account to the store, and got this message:

“The domain name of the email address is not valid.”

This e-mail account was already up and running when I started here. I think the person who set it up was the previous wine buyer that I replaced. Right now I’m (sigh) the most tech-savvy person in the store. A few months ago the owner needed my help to change the password. I’m also the only person who really checks and responds to incoming messages. If I don’t fix it, nobody else is going to.

Any suggestions?