If you use an automatic configuration script in your proxy settings, you might be experiencing this problem. If so, please vote on the bug. I don't think Adobe consider it to be important.
If your current version is older than 10.3.183.5, and if you are trying to use the Adobe Updater rather than going to their web site, you might be running into a bug that has already been fixed. Try going to http://www.adobe.com/go/getflashplayer/ and see if that works.
Or, if all else fails, you can download full installers. Although these are provided for distributors they can still be used to install Flash on a single machine.