BATON ROUGE (AP) — Abortion-rights advocates hope Louisiana’s near-total ban of the procedure will soon be blocked again, after plaintiffs in an ongoing legal challenge filed an appeal with the state Supreme Court Thursday.

Access to abortion in Louisiana has been back-and-forth for weeks, with the state’s three clinics relying on court rulings and temporary restraining orders to continue operations. Louisiana’s abortion law, which does not have exceptions for rape or incest, is currently in effect. However, if the Louisiana Supreme Court sides with the plaintiffs in their appeal, then enforcement of the ban will once again be blocked.

“We hope the Louisiana Supreme Court will rule that district courts have the power to block unconstitutional criminal statutes, including the trigger bans in question,” Joanna Wright, an attorney for the plaintiffs, said in a written statement Thursday afternoon. “Louisiana women must have access to critical and sometimes lifesaving healthcare, and we will continue challenging the Attorney General’s attempts to undermine that access through unconstitutionally vague statutes. This fight is far from over—we are not going anywhere.”

The back-and-forth battle over Louisiana’s ban began in June when the U.S. Supreme Court ended constitutional protections for abortion. While the plaintiffs don’t deny the state can now ban abortion, they argue that the law’s provisions are contradictory and unconstitutionally vague. The legislation bans all abortions except if there is substantial risk of death or impairment to the patient if they continue with the pregnancy and in the case of “medically futile” pregnancies — when the fetus has a fatal abnormality.

At issue is a legal question over whether district courts must put their rulings on hold while their decisions are appealed.

On July 21, Baton Rouge Judge Donald Johnson issued a preliminary injunction that allowed clinics to continue providing abortions while a lawsuit over the ban plays out.

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But procedures came to a screeching halt last Friday when a state appeals court ruled in favor of Louisiana Attorney General Jeff Landry, granting a “suspensive” appeal and ordering Johnson to reinstate enforcement of the ban.

Following the decision, Wright said it was disappointing that the First Circuit ruled without first allowing plaintiffs an opportunity to file opposition to the motion. She said the court “essentially eliminated critical health care services in the state.”

The plaintiffs are now challenging the appeals court’s decision in the Louisiana Supreme Court. If the court rules in favor of the plaintiffs — which includes a northern Louisiana abortion clinic — the ban would be blocked for the third time since the U.S. Supreme Court overturned Roe v. Wade.

The plaintiffs argue in their appeal of the First Circuit decision that providers don’t know what medical care they can perform under the law, and therefore “are forced, in tragic instances, to choose between engaging in potentially illegal conduct or refusing to provide critical healthcare to their patients with potentially grave results.”

The law states that doctors and others who perform abortions could face up to 15 years in prison.

Former Louisiana Attorney General Buddy Caldwell and 22 law professors in the state filed amicus briefs in support of the plaintiffs’ appeal. The briefs focus on the legal arguments of the filing and not the “merits in the underlying lawsuit.”

Abortion providers and advocates say each day of the ban being blocked has been extremely valuable. Since Roe v. Wade was overturned, there have been at least 249 abortions in Louisiana, according to data from the state’s department of health.