Citroen Xsara Picasso, year 2000, intermitant flat battery?

My Citroen Xsara Picasso is suffering from an intermitant flat battery - normally on icey mornings.
Most other times (in milder weather), it starts first time.
Have taken it to a 2 garages but they can not find root cause.

Even on icey mornings, it will start first time and then it will trvel for a few miles, but once the engine stops, it will not turn over - due to a flat battery

Kerry Mapps
February 2009