It could be the alternator failing, but it could also be something electrical staying 'live' when the ignition is off (phone chargers, non-standard sound systems and boot lights are very common causes) and draining the battery.
It might just be that the battery is old or damaged and is no longer holding a charge.
It's fairly easy to check, do you have/can you get a multi meter and do you know how to use one?
digger, October 2009