A friend of mine, Sébastien (@sarbogast), left his AR Drone battery charging for too long.
It sounds like the charger is not detecting when the battery is full and it keeps charging until you remove the battery.
This is really dangerous as the battery could explode.
Here's a picture (taken by Sébastien) of the battery. Hopefully, Sebastien did not need to call the fire fighters.
I then decided to recommend him to use a Lipoly charge bag * when charging his batteries to prevent damages caused by a battery on fire.
* The links provided are for EU residents, you will find the corresponding links for Hobbyking's international warehouse at the end of this post.
You may also use another battery, with higher capacity (meaning more flying time), with your Parrot AR Drone (v1 or v2). I recommended Sebastien to use this Turnigy 1300mAh 3S 20C Lipo Pack:
To be able to use it, you will have to use a cable adapter: Female Mini Tamiya <-> Male XT60 . I've seen people complaining that the cables (red and black) where inverted (reversed polarity) on the female side (Mini Tamiya connector). Make sure to check this before connecting to prevent any damage.
Finally, you may want to buy a better battery charger (like the "Turnigy Accucel-6 50W 6A Balancer") that will optimize the life of your batteries:
You will need to add a power supply as the charger does not come with one.
These are the links to use for non-EU residents:
All the links are provided to help but they also contain an affiliate code that will allow me to receive a small discount on my next purchase, you won't pay more by using those links.