Most likely, the coordinates are changing but you can't see them changing because you're zoomed in pretty far and the change is small enough that it doesn't register in the coordinate display. You can change that by setting your data view to show more decimal places in the coordinate display under Customize > ArcMap Options. Change this number to 6 or 8:
If increasing the number of decimal places in the display bar doesn't really help plus the data appears to no be in the correct location relative to other data layers, check whether the data layer has the correct coordinate system. A data layer that should be using a geographic coordinate reference system, latitude-longitude, with values in decimal degrees, will act this way if it has a projected coordinate reference system assigned/defined.