SIUE fell to 5-5 overall while New Orleans improved to 4-4.
"While this match was close at 4-3, it was definitely a disappointing loss," said SIUE Head Coach Jason Coomer. "This is one I think we let get away, but I credit New Orleans for coming out and taking the win."
Halverson won the most competitive match of the day with a 7-5, 6-7 (1-7) win over Amina Mrad at No. 6 singles.
Frogner improved her season record to a team-best 16-2 with a 6-1, 6-1 triumph over Marta Sans at No. 3 singles.
"Mia and Sierra did their part in giving this team an opportunity to win," said Coomer. "Unfortunately we just didn't play at the level needed to close out a match at this level."
SIUE opened the match by winning the doubles point. Halverson and Monique Krutak downed New Orleans' Grace Nolan and Yasmine Richard 8-5 at No. 1 doubles. Lexi Aranda and Haley Ilcewicz bested Hafsa Laraibi and Anna Degarra 8-2 at No. 3 doubles. Kali Donner and Mia Frogner went to a tiebreaker at No. 2 doubles but were upended 8-7 (7-3) by Soledad Calderon and Sans.
"Our doubles play was as steady as it has been all season," Coomer said.
SIUE opens Ohio Valley Conference play next weekend with road matches at Eastern Kentucky Saturday and Morehead State Sunday.