Try the Delete Identical tool.
WARNING - This tool edits the data in situ so make a back up before try this approach!
Here are some points (coloured by group ID), the black squares are the points remaining after running the tool.
So for example the green points have been reduced to 4 points.
Set the SHAPE field to be the field that is tested and then set XY tolerance. It is this value that you need play around with for your data. For my points 8m seemed like a good value to reduce the points, the higher the value the less points you will have.