I know myself and a few others were trying to find a fix for this issue recently. After a lot of Google searching and playing around with settings the fix I found was to change DNS settings. If you are updating by wifi (and get the c3-13340-1 error) then go to your Setting->Network->your wifi connection: Advanced. And change your Primary DNS to 184.108.40.206 and alternate to 220.127.116.11 and try and download and it should work. Likewise if you are getting the c0-11021-5 error and are attempting to update with the CMA then you need to go to your Internet connection settings (Control Panel\Network and Internet\Network Connections) and right click your network connection and click properties-> and find the IPV4 option, highlight it and click properties and set your primary DNS and Alternate to 18.104.22.168 and 22.214.171.124 respectively. Hoped this has helped anyone having issues with these error's they were a big headache for me.
The internet is out of my control, since my dad has the DNS and everything password protected. I checked the environment variables though, and there isn't anything for the Vita or the CMA. I could try adding them, if I knew what path to use, but I still don't know if it would work or not. It says it can't find the server, but it's installed on both the pc and Vita, so there isn't any server involved. I've never seen a problem like this and it's pretty asenine I must admit. I really wish it was just plug and play like any other device. But do you think the path variables would work? Or is there anything else I can try?
for those interested the dns servers suggested (126.96.36.199 and 188.8.131.52) are for "google public dns"
i have the servers are good, so i have deployed them to my entire network using my modem settings, so if its set on your modem/router you connecting to, there is no need to set them on the device, you are good
3g users winn need to enter it manually if downloading via 3g
I tried those , did not work , but i found another solution by synching my iphones 3g connection to the laptops wi-fi . so my carrier 3g became my wifi router , then i connected my ps vita to the laptop via usb and chose the update via usb and BAM!! it is working right now. but dont try it if your 3g connection is limited or expensive.
Have a nice day.