Four out of 10 council members were in attendance Thursday, not enough for a quorum, meaning no meeting and no votes on city business.
Jamita Swearengen, Joe Brown, Patrice Robinson and Martavius Jones walked out of Tuesday's meeting in protest.
Their candidate for the seat, Rhonda Logan, has been unable to secure the seven votes needed for the appointment.
The other candidate, Lonnie Treadaway, withdrew his candidacy Wednesday in another failed meeting, leaving the door open for some type of compromise.
The council members at the meeting said the District 1 appointment vote could be moved to the heel of the agenda so they can move on with city business like approving MLGW's budget and approving grants for body armor for Memphis police.
“To my colleagues who are not with us, we need to have this conversation, put away put aside your thoughts and feelings and come back and have this conversation,” said District 2 representative Frank Colvett. “It is getting to be embarrassing.”
“We have elected officials that have chosen not to show up and do their job because they didn't get their way, that's sad,” said District 9-2 representative Ford Canale.
The standing meeting resumes Friday at 4 p.m.
Council chair Berlin Boyd was not there Thursday afternoon, but told WMC5 earlier that he did not expect there to be a quorum.
He said on Wednesday that he is willing to extent the standing meeting to the weekend.