A few users are complaining on GBP Community Forum that they are seeing issues with Google Business Profile Messages.

They are reporting that they cannot open/see messages on Google Business Profile Manager, and even if they see the message, they cannot reply.
It appears that this issue started on January 5th and all the cases I came across are multi-location businesses.
A Product Manager already spoke with Google to open an investigation.
For updated information on Google Business Profile issues, solutions and notifications when issues are resolved you need access to GBPedia Guide.
To learn the latest about Google Business Profile (Google My Business), you should check these articles:
- If Google has suspended/disabled your Google Business Profile, should you create a new Google Business Profile?So your Google Business Profile is suspended or disabled and […]
- Google Business Profile Guidelines and RulesThis article shows the Google Business Profile Guidelines and Rules […]
- How To Fix Your Google Business Profile Suspended Because It Was Flagged For Suspicious ActivityI wrote this guide to help you if you have […]