If yet actual, that fix this problem can with add header Referer.

For example this http request returned error (Token, session and password replaced to star (*)):

POST /login HTTP/1.1
Host: www.factorio.com
Connection: keep-alive
Content-Length: 179
Content-Type: application/x-www-form-urlencoded ...

Then I will allow myself to show my simplest PowerShell script

#Factorio autoupdate powershell script

$useExperimentalVersion = 1; #0 - Stable; 1 - Experimental;
$baseTempFolderPath = "D:\Temp\";
$gameFolderPath = "D:\Temp\Game\";
$userLogin = "";
$userPassword = "";
$useSeparateGameFolder ...