Just to follow up: Our Geometry Service is ArcGIS Server version 10.1. I tested out using the ArcGIS online Geometry Service and the buffering worked with no issues. So, looks like the issue was with our Geometry Service, or our maybe our version of ArcGIS Server isn't compatible (?). We will use the online Geometry Service until we upgrade to 10.3 in a few months. Hope this helps someone else.