Q.
My instrumentation amplifier works at lower gains, but it can't seem to reach the desired output value at higher gains.
----------------------------------------------------
A.
You are probably running into the input common mode voltage vs output voltage swing limitations of the part. Internal nodes can saturate in instrumentation amplifiers using a 3 op-amp structure, thus causing a limit on the output voltage. This is demonstrated by the hexagon plot of an in-amp. An example hexagon plot is given for the AD8226:
Note that maximum output swing can be attained when the input common mode voltage is at half-supply. To know more about how this works, you can check this video. Page 2-3 of the the Designer's Guide to Instrumentation Amplifiers also discusses this effect.
To get the desired output, you can either increase your supplies or decrease your gain. You could also use an in-amp that can operate with common mode voltage ranges extending to the supplies such as the AD8237 or the AD8420.
