If you take point features from an SDE featureclass and put them through the PointOnAreaOverlayer, features coming out of the Point port can have the geodb_type set to geodb_polygon. This is because the original features did not have that attribute, so they inherit the attribute from the area. Then when you write them to a geodatabase, like a personal gdb, they get dropped because they have the wrong type to be written into a point featureclass. You get a "WARN | Came across an invalid polygon with fewer than 3 vertices. Skipping the polygon ...." Confusingly, the number of features that show they are written are the total number, not the actual number, so if you don't examine your output, you may not realize you're losing features.
The workaround is to place an AttributeRenamer on the point features with geodb_type set to geodb_point
This is PR#37731 but I haven't seen anything that says it was fixed so I thought I would note the fix for anyone else who might be having the same issue.