Hi, I have exactly the same problem. NBN satellite etc.
I have just posted this before I saw your post so will include it below. I have not found a solution so I have to continue to use the older and vulnerable version in Firefox which requires me to enable it when requested.
Win XP. Firefox 34.0.5 (latest)
The Flash Player download keeps failing with lost connection and then gives up.I am on a satellite Internet connection.
It seems to be extremely slow even when loading the installer which is only 1MB. Then when I run the installer and it starts to download the installation there are frequent messages about losing the connection and then finally gives up.
I have had problems with other software failing when I am on a satellite link. This is most likely because of the huge latency which may be taken as a link failure. Ping times are typically 800ms but can be 2000ms sometimes!
I have just received this from Adobe. I hope it will help.
The online shim installer, which you are using actually downloads and installs Flash Player silently in the background. If your satelite connection is experiencing latency issues it could result in the failure to download. Please try the full installer posted at the bottom of the Installation problems | Flash Player | Windows page, in the 'Still having problems' section.