typically the life span of a battery is around six years, there is a thread on here with many of us 2012 twizy owners having to replace out auxiliary battery, interestingly I heard Renault changing the aux battery on Zoe's also that are around 4 plus years old.
One of the first symptoms of a problem with the battery is a rotten egg smell. As the battery wears, some of the acid and water may evaporate which will disturb the mixture. This may cause the battery to overheat or boil, which will produce an unpleasant smell, and even smoking in more severe cases.
can you tell us a bit more about your twizy , is it in daily use , how often do you charge?
potentially there could be a problem with the charger providing too much current in to a depleted old battery.