Writing current position to EEPROM is possible, but doesn't compensate for the motor coasting to a stop or being moved when power is off. The best fix for the normal incremental encoder is to have a homing routine where you find a switch or a hard stop to "home" the motor after a power cycle.
If you can't use that approach, we offer two motors with an option for absolute battery backed encoders. The part numbers are SM23165MT and SM34165MT. For the absolute encoder you would add -FB01 at the end of the motor part number.
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