When you load a raster (or a shapefile) into your map, it is listed as a layer under the contents pane. Any changes you make here (like changing symbology, visibility, labelling) are properties of the layer and not the underlying raster or shapefile. Even exporting it, does not change properties of the layer.
So you need to save the properties of the layer (symbology, pop-ups, visisibility, definition queries, etc) as a layer file. Layer files are really awesome and I use them a lot.
Just right click on the raster under Contents pane, then go to Sharing>Save As Layer File. This will save a file with a .lyrx extension. Then the next time you want to load the raster, load this layer file and you will have your original symbology, pop-ups, etc.
