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It's using the IMA battery to start, the conventional starter is only used when it is very cold and or IMA is depleted. The auto stop is the main fuel saver on the car! Many vehicles use Auto stop now, some even use the conventional starter in a conventional car.

If Auto stop kills the IMA system, then you have a CR-Z with bigger issues! All CR-Zs work this way and it is deigned for this use and to last a long time. We have had maybe 5 IMA Battery failures and even fewer IMA motor generator failures, but @PeterPerkins can explain the system and allay your concerns better than I can.