I had that too a while ago.
I'd suggest to redownload the software (since it had an update) here:
http://esupport.sony.com/US/perl/swu-list.pl?mdl=PRS505.
After that you need to make sure you got the latest firmware on your device(the sony library software will auto-notify you about that).
It took me 2 times to make it work right (including a reboot).
I read somewhere on the web here that Sony was into the transition to a newer website, so I waited a day and the next day it worked perfectly!
What I prefer of the Sony Library above Calibre is that it has a good way of showing 2 pages next to eachother on fullscreen.
You can use it as a reader to read 2 pages at a time, where as Calibre just one page does not fit on my screen. (I have a resolution of 1280x800).
As far as the store everything works perfect, only it is a bit slow. Like it takes less then 2 seconds to load in my browser, and the library little more then 5 seconds.