Hi,
Thanks for your description of how you solved the problem. I am in the exact same situation with a Vaio 13 extended sheet battery which is only charging to 41%.
I can only assume that one of the cells has come loose also - however, I have no experience in soldering or any equipment to do it. Is it hard technically? Or would I be better off asking someone else to give it a try, although I'm not sure who I could trust to do this sort of work. I live in Australia.
Any thoughts would be great. Clearly the connections between the cells aren't that well made which is dissapointing because I really like the extended sheet battery.