MCP601 opamp common mode range

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You can expect either signal clipping or some increase of buffer output voltage above the CM range. According to the datasheet, no phase reversal takes place.
 
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some increase of buffer output voltage

do you think there's a possibility of the op-amp getting "railed" and staying railed even if the input voltage falls back into the common mode range?
 

You mean latch-up? Not if the input current is limited to 2 mA when exceeding the supply rails, and never if it stays within the supply rails.
 

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