Just started getting this error too after trying to resolve an 8002AD23 error that has been causing me to automatically sign out of PSN every 2 to 15 minutes since about the same time the 4.31 update was installed. It's happening more frequently now.
I only got the 80710D36 error when loading the PS Store while on wireless (I was testing to see if a faulty ethernet cable was causing the 8002AD23 sign-outs). Otherwise I could load the PS Store without trouble via a wired connection in a network, until I am logged out automatically a short time later.
So far I haven't been signed out while being connected to the internet wirelessly.
...So far. .__.
EDIT: lol 1 minute after writing this ...signed out of Playstation Network Error: 8002AD23 again. Not my ethernet. Not my network.
Just another day Sony likes to refer to as "Wednesday".
Nothing to see here folks. Move along. Take your dollars with you and buy that multi-platform game on that other network that doesn't go down evey holiday season with no communication from the overlords...