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If you overlay two maps and one or both maps disappear, or are not overlaid correctly, the most likely cause is that they are in different coordinate systems.

Look at the X and Y axes of the two maps before you overlay them. If the X and Y coordinates of the maps are vastly different (ie. one uses lat/long and the other uses meters), then when you overlay them, the points/map objects will either be on opposite ends of the map, or one or both maps may be so small that it looks like they disappear.

Make sure the maps use the same coordinate system and then overlay the maps. It may be necessary to adjust or convert the coordinate system of one set of data to match the other.

For example, see attached zip file. Unzip the SRF file and open it. The base map on the left is in latitude/longitude coordinates and the map on the right is in UTM coordinates (meters). Although both maps are for the same location, when you overlay them, the maps disappear. Convert the UTM coordinates to lat/long, or convert the lat/long coordinates to meters. Once both maps use the same coordinates, then use the Map | Overlay Maps command.