I belong to an HOA in Boulder. The boardis considering extending the minimal rental period from 30 days to 60 or 90 days. Can this be done?

You cannot prevent them from increasing the minimum rental period, no. You do have a right to be heard and can attend their meetings and weigh in on key issues. Otherwise you can wage a campaign to be elected to the board, and/or get enough people to disagree with the policy that will show up to the meeting, and defeat it by public angst.  It is fully within their power to do so, unless the articles state that they have to refer this to the HOA members for a general vote, but that would be unusual.