My 2005 Honda Jazz started to shudder from a standing start after 63,000 km. The dealer changed the transmission oil and rebooted the computer, which seems to have rectified the problem for now, but he advised the automatic fluid should be changed every 20,000 km. He also quoted $2000 to $3000 for a rebuild, but said some autos can't be rebuilt and that a new one could cost $5000 or more. We decided to get rid of it before it became a bigger problem and traded it in on a Mitsubishi Lancer 2008.
The first thing dealers usually do when they get a shuddering Jazz is to change the transmission fluid, which is a special fluid for the purpose, and that appears to fix most cars. In some cases it doesn't and in those cases it usually means the transmission needs replacing. Trading the car is drastic, but if that eases your mind then so be it.