"Use Wi-Fi in Power Save Mode" has nothing to do with the Vita being in sleep or your downloads pausing - it's a setting which allows the network hardware inside the Vita to run in power save mode, saving you battery at the cost of a lower quality, lower speed internet connection.
Unchecking it will up your wi-fi connection quality, and up your download/upload speed to the PSN.
As for your downloads pausing, I'm not sure why that's happening unless you're forcing the Vita to sleep. Pressing the power button to put the Vita to sleep ALSO puts the internet connection to sleep, you need to let your Vita fall asleep with the timer to have downloads continue in the background while it sleeps.