Hi Mark,
Yes, the B2 should remember your Wifi name and password. I have a B2 and a BB1 and both remember the Wifi names and passwords. If you know how to log in at Linux level, the Wifi details are held in a file called 'b2settings' under the tag 'Wifi'
On the BB1 this file is located in directory ' /media/sd3' and on the B2, the file is in /'/media/hdd1'.
So in normal usage, you should only have to key in the Wifi password on the first connection.
Are you using the 'Save' function after you key in the Wifi details?
On the B2, you activate the 'Save' function by pressing and holding down the 'Play/Stop' button until a 'SAVED' message appears on the B2's display screen.
Regards,
Peter