FFT bin interpolation for low frequency with DC offset
FFTs don't work well for sinusoidal frequency estimation if there is a nearby strong interfering signal.  Normally one needs at least 2 FFT result bins of separation to just start to resolve 2 frequency peaks.  For frequencies around or lower than FFT result bin +-2, any significant  DC offset will constitute that strong nearby interference (in bin 0) preventing resolving either frequency as an independent peak.

My guess is that, if the S/N ratio is low enough, a parametric estimator will produce a more accurate estimation, given that you have more samples than unknowns (3 sinusoidal parameters + 1 DC offset parameter).

Another possibility is to try to remove the DC offset by averaging or low pass filtering over a much longer window of samples, perhaps several hundred to thousands.

Added:
Strictly real valued sinusoids very near DC (or Fs/2) will also see interference from their own conjugate images in the spectrum.  Any input gain imbalance in the 2 quadrature components for a complex sinusoidal signal will contain some of that same conjugate interference as well.