A high gain is exactly what's required for amplifying small changes and a linear amplifier should have no threshold
I have tested this in practice. configured an opamp for a high gain, it does the job, but it looks like it does not amplify all inputs and it misses the ones which are below a certain threshold. We can say it is not sensitive enough for those ranges.
What does it miss? It seems like something else is going on.
Could it be the bandwidth is too low? Have you plotted the gain vs frequency?
Going from the
other thread the signal of interest is between 100Hz and 1kHz. Connect the output to an oscilloscope to monitor the amplitude and the input to a signal generator. Set the signal generator to a sine wave with the appropriate amplitude to give a clean sine wave on the output of the amplifier with no clipping and sweep the input frequency from 10Hz to 10kHz (I advise going in steps of 1, 1.5, 2, 3, 5, 7 i.e. 10Hz, 15Hz, 20Hz, 30Hz, 50Hz, 70Hz, 100Hz, 150Hz, 200Hz etc. to make life easier) and plot the amplitude. That will tell you whether your amplifier has the required bandwidth for the application.