If builder ceases operation during the developer control period, can the community take control of the HOA?

HOAs in Georgia are governed by OCGA sections 44-3-220 through 44-3-235.  Your options depend on (1) the wording of the Covenants and Restrictions governing the lots in your developement and the Bylaws of the HOA and (2) the status of the builder.  The easiest thing to do would be to have the builder transfer control to the HOA, but if they're in bankruptcy then they probably cannot do that.

Your problem is going to be 44-3-226(a), which states in part "Notwithstanding any other provisions of this subsection, during such time as the declarant shall own at least one lot primarily for the purpose of sale of such lot, no amendment shall be made to the instrument without the written agreement of the declarant if such amendment would impose a greater restriction on the use or development by the declarant of the lot or lots owned by the declarant."  As long as the builder owns the undeveloped lots, the HOA is essentially powerless to make any changes without the builder's written consent.

Feel free to contact me if you have any other followup questions, I've handled several HOA issues before.

You and your fellow homeowners need to seek consultation from a real estate attorney in your area as to what is happening to your new development.  It appears that your builder has probably filed for bankruptcy and this will effect your rights as well as the rights of your fellow home owners.  The attorney will need to read all the documents associated with the development and see how they relate to the rules and laws governing home owners associations in Georgia.  There indeed may be a way for you to file a petition to allow you to form your own home owners association at this point in time and to protect yourselves.  You all may also have to file in the bankruptcy court if there is something that was owed to you by the builder but was not done.  Seek help.  Good luck.