[i]"But when I'm at Zero Beat, and not playing it"[/i]
Am I correct in believing that at this time the volume is not being reduced - hand is away from the volume antenna - and that you are relying on zero-beat to mute the output ?
If the above is true, then the answer could relate more to stray fields within the Theremin than to external fields.. The volume amplifier (VCA) will be 'wide open' (maximum gain / minimum attenuation) - there will be interactions between the HF oscillators which, due to non-linearities in the amplifiers etc, could hetrodyne to produce low level beat frequencies - these may not be easy to hear when there is an (intentional) audio beat frequency being produced (in which case also, the volume is likely to be reduced, so proportionally also reducing these unwanted audio signals).
I have found many unexpected sources of unwanted audio 'noise' or 'interference' within my Theremin prototypes (another reason it is taking me so long to get my Theremin to market) and have been forced to concentrate on extensive shielding of radiating components, and to take EXTREME care with power distribution within the unit..
One 'simple' fix would be to have a filter and envelope follower tracking the pre-VCA signal .. If the beat frequency then dropped below (say) 20Hz, the VCA could be 'closed' (maximum attenuation) automatically.. something like a compressor, but without the latency, pumping, or other problems compressors and noise gates can cause.