I agree with WillWren, shutting off the ECC before disconnecting the battery is probably a wise thing to do.
Having said that, I don't think removing battery power is necessarily the cause of airmix actuator failures, but it does seem to exacerbate an existing or latent problem. Most likely, if you have issues after a battery disconnect, the problematic actuator gear prolly already had a crack in it. I suspect disconnecting the battery causes the ECC to go into a self-calibration which drives the actuator full cold and full hot so it knows where it is. I think when the door hits the closed or open position, the gear slips on the shaft which either enlarges the crack, or loosens the press-fit of the gear, or both. This, however, is purely speculation on my part - experience based, but speculation nonetheless.