There are different ways to handle this.
My advice would be to let the community back you up. Which does mean being part of the community and having people actually know you, the association staff, as individuals. I think this is a little bit more involved than Maggie's answer, but I also know her groups are pretty huge numbers-wise so it might not be so easy for ASHA.
ASAE does this very well - everyone knows people who are part of the staff there and who interact online and are friendly with members. I would say ASAE gets much less criticism than it might purely based on the fact that we would feel bad if we criticized them because we know that Lisa, or Peter, or Reggie, or Wanda, or whoever might be sad about it.
Of course this is a longer-term answer, but if you are able to be part of the community like that, then when contentious issues arise, more likely than not someone will come to your defense and you STILL won't need to respond from an "official" point of view.
Another thing you can do when there is constructive criticism is contact the "criticizers" (directly and privately or openly in response to the group) and just say that you are hearing what they are saying and (if necessary) taking steps to fix whatever it is. Often, complainers just want to know that they are being heard.