Did you Authorize the reader after opening a Sony Reader store account? With regards to logging out of the Sony program on your computer, you cannot. Once you start the program it automatically logs you in. Don't know why but you can't. That's the way they made it. Remember that registering for an account & authorizing are two different actions.
I agree with ATDrake in that I don't think your Adobe & Sony Reader store accounts are properly connected and that's the issue. It's most certainly not the device. It's user error here. We just have to figure out where.
Creating two accounts at the Reader store wasn't a good thing. Could you possibly have two Adobe accounts and maybe that's confusing things?
On the device go to Settings, Device Information. Does it say
Authorized for Adobe DRM?
On your computer open the Reader for PC or Mac (sorry don't have a Mac so hopefully it's the same). Go to the Store, then My Account what does it say under My Devices, Devices? Does it list the reader there? When I had both my 350 & the T1 I renamed them Pink 350 & Black T1 so I'd know which was which because I think it just called it some generic name. I can't remember exactly.