I don't see the information currently in the help documents but it appears the Google Posts you make in Google My Business expires around seven days later. As you know, a couple weeks ago, Google brought Google Posts live to most Google My Business owners and you can now easily post messages in your local panel instantly.
This is what it looks like:
But that message seems to last for a maximum of around seven-days.
Brodie Clark from Optimising shared a screen shot with me on Twitter showing an email notification he received from Google warning him a Google Post will expire soon, which was around seven days after he posts. Here is that email:
It does seem correct, as the original Google Post went offline late last week and I had to post a new one for something new to show up.
Forum discussion at Twitter.