Hi Jason,
Oh, I hate that canned message from Google! If you do a search for the language of it in the Google And Your Business Forum, you'll see it's one Google sends out in a ton of different situations. I am not currently seeing a mass influx of reports of this message in that forum, but that doesn't necessarily mean there isn't a mass issue going on. Some questions:
Did you recently make any changes to listing?
Are you still able to access the listing via the dashboard? If so, are there any messages/warnings?
If you can access the listing, have you tried performing a null edit? If not, it might be worth a try. (In case you're not familiar with this, all you have to do is log in, hit the button to edit the listing in the dash, don't change anything, but then save as though you have made a change). In some cases, this can refresh the situation and resolve some problems ... but only in some cases.
How did you receive the above message from Google? How did you report the issue?
Regarding the question in the title of your post, if you've received an email from Google, you have, in essence, already heard from their engineers. Three weeks is definitely not an adequate amount of time for things to get rectified in Google land, but that doesn't mean you can't attempt other methods of flagging their attention. Here are 2 suggestions:
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Go through the troubleshooter that leads to a phone call. Click the Contact Us link on this page while logged into the account associated with the listing: https://support.google.com/places/#topic=1656871 Proceed via the blue 'Call Us' button.
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Start a thread in the Google And Your Business Forum begging for help from the Top Contributors there who have the ability to escalate your issue to Google staff, if they so choose. https://productforums.google.com/forum/#!forum/business
It may be that you will just have to wait this out. Without knowing the details of the business and the situation, I can't offer any more specific advice, but I do think it would be worth it to try one or both of the help options I've described. I'm so sorry you've received that dread message. What a headache. Good luck, and if you get this resolved, it would be nice if you could update this thread with how things went.