Can't explain why but I think I can help you get them moved. I noticed an oddity when using a crossing window selection of a point. Properties panel lists (2) cogo points that are identical (this is "bad"). You should not be able to have (2) points with the same numbers!? Just for kicks try moving a single point a few feet, there should be a point left behind, regenall, point left behind disappears. Also try select similar of a cogo point, I was receiving a count of 974 but your "all points" group only lists half of that count of 487. Possible solution, export ALL point group out of drawing, delete all points, reimport point file, move points to new location.