My county of East Sussex will probably not vanish any time soon. That said, my official postal address doesn't contain my county anymore so I only give it out when a form marks it as "required".
My family is in West Sussex

No I don't think either would. I believe Middlesex was folded into Surrey because of its size (ie, lack of population) in relation to the others around.
Ditto on the official address, I live in Farnborough and there are a lot of places in the UK with that name, so I often put "Hants" or "Hampshire" after the name, but the Post Office does not require it.
Their postcode checker website can give you the full official postal address. Often useful.
James -
be* pro - 16.8mbps sync -
BQM
FTTC cab arrived 18-jun-2012 (due Mar 2011) - Openreach estimate 44.6Mbps / 6.5Mbps