The recommendation would have had the board conduct an investigation of underlying conduct described in a protective order the Travis County District Court issued in July.
A one-page memo from Faltys attached to the board agenda also recommends the hiring of an external investigator.
The board's decision to take no action came after three hours of executive session.
Returning from executive session, the board announced that it called a meeting for Jan. 6, when it will again consider whether to place Azaiez on administrative leave pending the outcome of an investigation, consider engaging the services of an independent investigator and the appointment of an acting superintendent followed by a search for an interim superintendent.
Community members spoke ahead of the board's decision with some asking it to approve the recommendation. One community member, Mike Williams, asked the board to consider the recommendation a "lifeline" for the quelling division in the community.
"The TEA has presented the Round Rock community the opportunity to start to heal," Williams said. "That decision is up to you folks. It takes four of you to reach out, grasp that lifeline, so that the temperature will come down and we start to resolve this thing."
Others, such as Elaine Li, asked the board to let the investigative work be carried out by local authorities.
"I do not support putting Dr. Azaiez on leave," Li said. "Let the proper authority investigate, and let the due process play out. We live in a system that assumes one is innocent until proven guilty."
The board originally voted 5-2 on June 14 to hire Azaiez as superintendent for a three-year contract with a $350,000 annual salary.
Community Impact Newspaper reached out to RRISD for comment regarding the recommendation from the district's monitor but did not hear back as of press time.
This is an ongoing story and will be updated as more information becomes available.