The 2015 model Jazz was recalled for a CVT transmission problem which could see high internal hydraulic pressure cause an internal shaft to break, at which point the car would lose all drive. However, your 2005 model Jazz was not fitted with a gearbox with the same potential problem.

Even though there was no recall for the 2005 Jazz's transmission, those with the CVT transmission could suffer shuddering problems which were linked to depleted additives in the transmission fluid. The solution was an improved fluid which was added to the gearbox once the old fluid had been drained and the car's ECU reset. While Honda dealers were performing this change, the problem was not deemed to be a safety issue, so no recall was issued.

The Australian Federal Government operates a website that lists all recalls for all makes and models officially sold here. It makes for some interesting reading. You can find it here.

A few factors determine engine longevity, so let’s start with the first of those, the basic materials and design of the engine in question. Both the Toyota and Honda have advanced small-capacity engines that are made from quality materials. So that’s in their favour.

The second factor is servicing. A lack of regular maintenance including fresh oil and filters will kill engines fast, so that’s crucial. And finally, how they are driven will also play a part. An engine that only does long distances in the country will always last longer than one that is subjected to frequent cold starts and stop-start traffic. An engine that is regularly revved to redline between the gears will also potentially die younger than one that is driven sensibly and with a bit of mechanical sympathy.

The bottom line? There’s no short answer. But I have seen small-capacity Honda and Toyota engines clock up 250,000km and more with correct maintenance. Things have certainly changed from the 1950s when the average car engine needed a rebuilt every 100,000km and what was called a de-coke and valve-grind every 30,000km. Ask your grandfather about it.

It's a problem with the CVT transmission and one that Honda is   aware of and has been rectifying. Take it back to your dealer and   have them assess it. They might be able to fix it by changing the oil   in the gearbox, but in some cases they have replaced gearboxes.