It is quite unusual for some movies to get Poster Art, and some not. Unless TheMovieDB doesn't have Poster Art for the movie, but the fact you can get it by running the "Get Movie & TV Show Info..." function shows that it has the Art.
Usually you either get all data, the metadata (tag) and image, or no data. As long as MC is set to get the image. There was a change in MC recently so that the tick box setting "Use Image" or "Get image" is now remembered and shared between single and multiple movie lookups, and I think also with the Auto Import feature. But again, that should work for all movies, or none, unless you are changing that setting sometimes, not realising that it would affect Auto Import.
Overall I find it very reliable, for all data.
But if MC is downloading the metadata for the movie, and that is correct, it should be downloading the Poster Art as well. In your case I would suspect a slow internet connection, causing a time out just on the image download, or possibly a problem with the site itself, perhaps it is being overloaded at the time your Auto Import runs. I assume that you have the disk space available for the downloaded images.
Maybe provide some examples of the filenames of the files you are importing, for others to test if they work for them.