Integrated Motor Assist (IMA) battery failures are not uncommon. The IMA battery will require replacement when it fails.
2005 Honda Insight Problem Reports
Most Reported 2005 Honda Insight Problem Reports
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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.