Integrated Motor Assist (IMA) battery failures are not uncommon. The IMA battery will require replacement when it fails.
Resources for the Repair and Maintenance of your 2005 Honda Insight
2005 Honda Insight
2005 Honda Insight Problems
The automatic transmission (CVT) can have a "shudder" due to a worn start clutch. Replacing the start clutch should correct this type of shudder condition.
IMA computer software failures. Depending upon the computer it will have to be replaced or updated with a software update from Honda.