In the end I was able to track down the issue. If I use the Intel’s Math Kernel Library (MKL) by giving the command: FFTW.set_provider!("mkl"), I observe the issue that appears for 47499754 points.
If I switch back by means of the command: FFTW.set_provider!("fftw")
the missing amplitude signal appears. Issue is solved 
Another observation is:
If I use rfft() instead of fft() the fft-algorithm can handle 47499754 points, even if I turn on the MKL
The code snippet for rfft() is:
# --- RFFTW -------------------------------------------------------------------------------------------------
amplitudes_rfft = abs.(FFTW.rfft(td_data_))
amplitudes_rfft = amplitudes_rfft[1:end-1] .* (2/window_length)
amplitudes_rfft = amplitudes_rfft[2:end]