Apparently, most wireless devices are configured to power down after a certain amount of idle time, where idleness is measured by activity at the keyboard or mouse, not activity on the interface. If you would like to leave your computer down/uploading content while you go do something else, you will be disappointed.
The following commands should turn off power management on the wireless interface (replace wlan0 with the name of your interface, found with iwconfig). Note, the last command may not be necessary for your device, returning an error such as Operation not permitted with no serious consequences.
sudo iwconfig wlan0 txpower fixed
sudo iwconfig wlan0 power off
sudo iwconfig wlan0 commit
To make this permanent, add these commands (without sudo) to the /etc/rc.local file.