I had posted thread same here, but FiveFourteen recommended me post this problem at here because this is support box.
I will quote things I post in old thread. I'm sorry if I'm wrong, please correct me. Thanks!
Below my contents:
I'm new bought PS Vita and I download game demo on PSN. But I very uncomforable because PS Vita auto disconnect wifi when screen auto off.
In setting section, I can't see options DISABLE "power save", it's shows 1m, 2m, ... 10m (I has choose 1m)
So, I access PSN and get free demo game and waiting for complete, a few minutes, screen off.
I press PlayStation Home and check on screen, I see notice PAUSE, I have to select Resume All.
How can I solve that prolem: I want permanent wifi up, not auto off, standby, save mode any more?
And now, I really don't know Sony OS bad or me (sorry for that if I wrong)?
This is working as designed. When the Vita is in standby, it will turn its Wi-Fi radio off to save power when it is not actually accessing the network (which is does every 20 minutes or so to pick up messages and updates). There is no way to disable this behavior. Normally it should not be a problem, as the Vita saves the Wi-Fi access credentials, and can reconnect to the network as needed. The Wi-Fi radio uses a significant amount of power, and the amount of time that the Vita could run in standby before it needed charging would be significantly reduced if the Vita stayed connected to the network all of the time. Why do you want it to?
I answered in the other thread so I'ma just paste it here.
"Someone posted about this recently. A good work around is to make a skype account and keep skype on in the background while you download. The vita will still sleep but the download will continue due to skype running. I was randomly having this same problem but this method works 100%."
Basically make a skype account start the app up and the Vita will keep a wifi connection so downloads won't quit during standby/sleep.
Easiest fix in the world right there yo.