Connectors only 'connect' to certain points of objects and groups. Below is a list of kinds of objects and the points on them that connectors will connect to.
Lines: endpoints, midpoints
Squares, Rectangles,Notes, Text frames: line endpoints and midpoints, object centerpoint
Circles, Ovals: 3, 6, 9 and 12 o'clock and centerpoint
Rounded rectangles: line end and midpoints, and the endpoints and midpoints of the arcs that make up the corners, and the centerpoint of the rectangle
Smoothed polygons: endpoints and the midpoint of the polygon
Unsmoothed polygons: any control point on the polygon
Groups: Group centerpoint, group cornerpoint, and the midpoints of the bounding rectangle lines of the group
Connectors: Cannot connect
Framed models (tables, data charts, calendars, time lines): Frame endpoints, midpoints and centerpoints of models
Unframed models (org charts, flow charts, outlines): frame end- and midpoints, centerpoints or models
You can connect to other points in a model if you ungroup the model. To do so, cut the model, paste it, and ungroup it. The model will become a graphic object and you will not be able to use any of the model commands or functions, but you will be able to connect to points on the objects.