Moving to Instrumentation Amplifiers community.
It seems that you are running out into diamond plot limits. Please see this FAQ about input common mode voltage range of inamps.
Also, AD8221 doesn't have much operating range when it is powered on 5V single supply. I would recommend to switch on AD8422 instead for wider operating range. I also recommend to use this tool to check if your input conditions are within the specification of the parts.
By the way, what is your applications and why do you chose the AD8221?
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