Rasters exported from QGIS (via Save As > Rendered Image) do not retain original styling. See attached. Any thought on how to prevent this error? The top image is exported from QGIS as a .bmp, the bottom is a screen grab from tilemill. Thanks. 
[GIS] Why does Save as “Rendered Image” change the raster styling
qgisrasterrendering
Related Solutions
You can do that in Python Console of QGIS by using a QgsRasterPipe object (pipe) for setting a renderer clone of the image employed as active layer before to use the 'writeRaster' method of QgsRasterFileWriter class (you don't need gdal_translate).
I used the following code:
layer = iface.activeLayer()
extent = layer.extent()
width, height = layer.width(), layer.height()
renderer = layer.renderer()
provider=layer.dataProvider()
crs = layer.crs().toWkt()
pipe = QgsRasterPipe()
pipe.set(provider.clone())
pipe.set(renderer.clone())
file_writer = QgsRasterFileWriter('c:/pyqgis_scripts/output2.tif')
file_writer.writeRaster(pipe,
width,
height,
extent,
layer.crs())
To test it, I loaded a raster dem (sample_dtm.tif) at the Map Canvas of QGIS and then, it was rendered as a singleband pseudocolor layer with 5 classes (see below image):
After executing the script, the rendered raster (output2.tif) was saved with the espected renderer; as it can be observed in the below image (compare the thumbnails of sample_dtm.tif and output2.tif) when I load output2.tif raster at the Map Canvas. The renderer was effectively cloned in output2.tif raster. The code works.
I assume the GeoTiff is in WGS84 EPSG:4326 with degrees as units. As you may know, degrees of latitude and degrees of longitude have different lengths if you are away from the equator.
What you expect to see is a projected CRS, like Web Mercator EPSG:3857 or the UTM zone of your part of the world. In QGIS, you can set the project CRS to change the view using Project -> Project Properties, CRS tab and enable on-the-fly-reprojection, without changing the GeoTiff's projection.
Best Answer
When you save your raster layer as
Rendered imagefrom QGIS, the saved image quality depends on your choosed profile parameters. Please, check your settings to find which of them alters your output quality: