......explained a bit further for Hearing Aid Forums readers.
That's not static, it's the noise floor - caused by air particles hitting the diaphragm of the mic (Brownian motion).
The 'only' (perhaps somebody else has now) people to have dealt with this properly so far are Widex. If you're an engineer you'll get the explanation.
All* the mics used in hearing aids are based on the electret condenser principle. You basically charge a gold/mylar film to a high voltage (permanent) and then move it back and forth over a backplate. The back plate is connected to a MOSFET gate which allows the incoming voltage to be 'switched' on and off. Hence your mic signal. The diaphragm mass is as small as possible to reduce skeletal vibration transfer and be as sensitive as possible. It's also got to be as near to the back-plate as practical to ensure the best attraction/repulsion.
The downside of making the diaphragm smaller is that the effects of Brownian motion become more pronounced and you create a noise floor of 20-30dB before the amplifier stage, especially with the smallest diaphragm mics.
Widex uses a clever system to get around this - by splitting the input (1.0-1.2V) voltage at x GHz into an AC voltage it creates an effective 2.0-2.4V potential across the aid. Which you will know benefits the system as V rises, power consumption falls. The particular benefit with this system is that higher voltage allows the mic diaphragm properties to be altered - moved away/different mass - which can be used to alleviate the effects of Brownian motion. Subsequent noise floor levels are now around 16dB.
Furthermore the Widex system is 16-Bit (96dB range) and only starts sampling at 17 dB - so the entire mic is effectively ignored by the hearing aid UNTIL it starts producing a signal in relation to a real output.