It already does, It saves the settings to the Memory Card, it works fine for me anyway.
Do one thing, change those settings, and go to Configure / that is below Browser (mayb i'm wrong whether its called configure or not), anyways, play with the settings and quit that area ( go back to main screen) then start a game. Hopefully all the New settings will be saved. Reset the PS2 and then check, i seem to have no problems
My version of the PS2 will not save the psx driver settings, so I would need to configure it every time. I haven't seen anything that "fixes" this, it would need something like upgrading the bios, and that can't be done (AFAIK).