I checked on the line input to the Sony PCM-M1 and it has a 20% 10 uF tantalum chip capacitor in series with the signal path and a 47k input impedance, so it's got about a .3 Hz bass cutoff frequency on the input. So, my suspicions about being related to signals near the cutoff frequency are probably not well founded. However, it's still a coupling cap whose instantaneous capacitance is affected by the instantaneous input voltage and that is going to modulate the gain of the front end slightly, though not to the degree you're showing in your picture.
When I first looked at the picture of your waveform, I did not realize that the vertical scale was in dB. I'm only showing maybe 1 dB or 1 1/2 dB of difference in level between positive-going and negative-going signal peaks on my old PCM-M1 recordings and your recording is showing more like 4 or 5 dB, so you've got something more drastic going on.
My first ever recording was with a borrowed rig (AT-853 mics and SP battery box into a Sony MZR-37 miniDISC recorder) and it had distortion that looks (and sounds) very similar to the recording you've posted. My battery was brand new that night and I checked the voltage later and found that it was just over 9 V.