Thanks for the info. After reading Google’s FAQ and additional info, it seems that they not only block geocoding results for too much volume, but also for too much speed (I guess too many requests within too short a time). Since this site is not on a shared server, the only thing that made sense was the speed of the requests.
I didn’t want to go backwards by adding any manual steps into the process, so I enhanced my php code. In my loop that adds the POIs, I first check for new post meta fields containing the latitude and longitude. If found, I create the POI with the point. If not found, I geocode with the address and if I receive valid results, I add the latitude and longitude as post meta fields for use the next time.