In short, Google allowed business owners to reply to reviews within their Google Place pages. But it didn't work for all and the issue was supposedly resolved at least once, but was not. Around three months later, Google finally told us in a Google Places Help thread that it was resolved, once again.
Stephan from Google said:
We've rolled out an update today that should resolve this issue for users that were having technical issues posting owner responses. Responses that did not show up on your listings after posting should have been restored.
If you are still experiencing issues with this feature please be sure of the following:
1. That you've verified your listing using Google Places .
2. That you're logged into the Google account that has claimed the listing you are trying to post the response for.
If you are still experiencing the issue of being able to post a response but the response not showing up on your listing please let me know on the attached thread .
I guess we will find out for sure if it was fixed or not. I certainly hope it was.
Big hat tip to Mike for staying on top of Google about this.
Forum discussion at Google Places Help.