What if you set that option to something else, back out, then change the setting back to Always On? Maybe it will rewrite the config file and kickstart it into working.
Seems odd though, my nexus continues to download when the screen is off. If you have access to your router, can you see the phone drop off the network? Might be something to try...figure out the IP address of your phone, then on your PC, ping it with the command:
ping -t IP_Address
Then turn the screen off. If the pings stop completing, then you know that the wifi is turning off because of that setting. I wonder if it's a hardware issue since others' phones don't seem to do that normally.