wild stab in the dark, but if you're using QGIS you need to ensure that the layer containing the points is highlighted in the layers list for the selection to work.
Same I believe goes for ArcGIS (i.e. the layer needs to be highlighted in Table of Contents).
In MapInfo you need to check that the layer is 'selectable' in layer control, and be aware that MapInfo will drill down through the layers in your workspace (top down) until it finds something that it can select, therefore if a layer located higher in the layer control is selected, the selection will not get down to your point layer.