Rescind Bylaws?

Can bylaws adopted at this month's meeting be rescinded at the following month's meeting? We were told that they could not go into effect until approved by the national organization.

No.  Bylaws can only be adopted according to the requirements in your organization's bylaws.  Most bylaws have an article on amending the bylaws.  Amending means adding new language, changing existing language, or rescinding existing language.  Usually, bylaws will require previous notice and a two-thirds vote for amendment.  Thus, to rescind the bylaws that were adopted at this month's meeting, notice must be given before the next meeting and a two-thirds vote must be attained at that meeting to rescind what was already adopted.

There may be other special provisions in your bylaws amendment process, such as having a committee review any proposals beforehand.  If any such provisions are laid out in the bylaws, they must be followed.

As for approval by the national organization, this may well be a requirement for your organization, according to national requirements (see the national bylaws).  Technically, the bylaws for your organization go into effect as soon as they are adopted.  If the national organization requires approval and does not give it, then there could be a challenge to your organization's affiliation with the national organization.  Most national organizations will help subordinate affiliates in drafting their bylaws.

Sometimes, it can take some time to get bylaws in proper order and approved by the national organization.  Patience and persistence is the key.