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Ever since Sony copied off Xbox's layout, and made it more difficult to manage, and "Broke" facebook Sharing, the Playstation Network has been much more unstable on the store. If I download more than 20 things at a time, I get said error. I have to shut off my PS3, and restart it, to allow more downloads. I have 2007 downloads on my list. I wish that we weren't forced to upgrade to the new Playstation Store, I NEVER had these problems with the old layout. It's also much harder to browse categories unless you know exactly what you are searching for. The old layout was much cleaner.
Yeah I am getting a ton of these errors. Mainly because my HDD couldn't recover from an integrity check and I had to reformat and re-download all my PSN stuff.
It'll spit out 80710003 after queing/downloading a total of what appears to be ~20 items. Sometimes it happens at a lesser number. All you can do is quit the store. It looks like you're still logged into PSN but you're not. You can't synch trophies, update games, or anything. All will give 80710003. And signing out won't let you sign back in it'll give 80710003 again. You need to reboot the PS3 to get back up and running.
And fwiw, it happens on both PS3's in my household. 1 is 2 years old and the other is brand new.
Use the Support/Knowledge Base if you have error codes
the error code suggests it is an issue with your wireless signal. try resetting both your modem and router by leaving the power to them turned off for one minute, turn the modem back on first until all the lights are steady and the modem is "waiting".... then power on your router.
then power your PS3 on.
I have gotten this code a few times. All you need to do is log out of the store and shut your playstation down. When you restart it n go to the store it will be fine. Have no idea why it happens i jus know how to fix it.