Op-amp unexpected behaviour; amplification regime breakdown
That's a very low impedance feedback path for an ultra-low power op-amp. The output resistance is probably of a similar order to the R1 which is causing you problems (you can 'measure' it from the SPICE model, they typically don't discuss such dirty little secrets on the datasheet). 

I would suggest increasing it by at least an order of magnitude, taking R2 to 1K and C1 to 10nF, preferably by two orders of magnitude (R1-> 10K and C1->1nF). Gain is specified with a 50K load to ground.  

Check your calculation of the C1 value too- it should have negligible reactance at 3.8KHz compared to R2, so I get more like several uF than 100nF for R2 = 100\$\Omega\$. So maybe 10K/39nF for R2/C1 and R1 from 0 to 2M