I have had exactly a similar problem since new in 2014.
I noticed from new that the voltage on the battery (Varta originally) declined steadily over time and therefore I charged the battery once a month. I was surprised at the first service that the voltage was 12.43 volts and I was equally surprised to be told by the dealer they had seen worse!
I never had a sensible voltage reading on the Jazz so I bought a new Yuasa. At the same time I purchased the same battery for another car.
I found I had the same problem with the Jazz despite the new battery. The other car's battery retains its voltage perfectly.
I checked the residual current drain on the Jazz and it is 20 milliamps ie normal (if not good!).
The alternator charges at the correct voltage.
The Jazz does many short journeys of only 3 miles or so. The other car does at least one continuous journey of 15 miles per week.
My conclusion is that, by charging the original Varta battery on the Jazz, I was hiding the problem.
The Jazz either needs a non stop journey of, at least, 15 miles each week to keep the battery in good condition - or a recharge of the battery once a week, which I now do.
The battery in the Jazz used regularly for many short journeys never gets fully recharged and thus declines until it gets below the level that would start the car (i.e. flat battery) - which is a little curious for what is a town car.
So, nothing is wrong with the Jazz, as such.
It seems, simply, down to the way the car is used.
Hope this helps.