The measure command has an option on the Command Bar to set the keypoint filter preference. If you cannot select a keypoint it is probably due to the filter restricting it or if in an assembly, the part you are trying to select on is inactive. Smart Measure's filter is at the right of the Command Bar...
You'll need to use the "Distance Between" dimensioning tool to get the options you're looking for....make sure all of the "IntelliSketch" options are checked on.
Design Manager Streetscape Limited
Solid Edge ST10 [MP0] Classic [x2 seats]
I was assuming the 3D environment because it was not specified... You are right, the Smart Measure command in Draft does not have the keypoint filters, as per it's explanation, it only measure elements or angles between elements. If you want to measure between keypoints, you need to use the Measure Distance command which will access keypoints based on the Intellisketch settings... Or use the regular Dimension commands as Sean stated if you want them to persist.