With the latest audit offering a new perspective, Jackson Health System’s long-troubled finances are looking better in some basic areas, but underlying problems linger and a precarious future lies ahead.

After losing $419 million over three years, Jackson eked out an $8.2 million surplus in its fiscal year that ended Sept. 30, according to the audit released earlier this month, and its most recent monthly report, for January, showed a $5.5 million surplus.

“What a difference a year makes,” Chief Executive Carlos Migoya gloated to Jackson’s board on Monday . “We made the tough decisions,” which included laying off a thousand employees and collecting payments more quickly.

But he didn’t try to sugarcoat the future. “We have a clear picture of our challenges.”

Those challenges include finding new ways of attracting paying patients, attempting to repair Jackson’s strained relationship with the University of Miami, finding hundreds of millions of dollars to fix up its aging facilities and adjusting to state and federal healthcare reforms that could cause Jackson’s poor and uninsured patients go to other facilities.

“We’re literally in the calm before the storm,” said Marcos Lapciuc, Jackson’s board chairman.

Up to this point, Jackson’s turn-around has been funded by cost-cutting. That has resulted in “positive results,” said Sal Barbera, a veteran hospital administrator who now teaches at Florida International University, but it’s “unsustainable, as expense cutting has a limit and will not bring prosperity to the organization. Revenue growth will not be easy.”

Even the present remains tenuous. At the end of January, Jackson’s cash on hand — a basic measurement of money in the bank — remains a low 14.5 days, far below the 175 days of cash that executives want to have to ensure smooth operations. “We’re not going to solve that cash problem in one or two years,” Migoya said.

What’s more, the recently announced audit revealed a profound weakness in one often-ignored sets of figures: In fiscal 2012, Jackson’s current assets were $450 million, while its liabilities were $495 million. In accounting terms, Jackson doesn’t have enough money to pay its bills.

That’s why Joshua Nemzoff, a Philadelphia hospital consultant who used to live in Miami, says, “They continue to be in very serious trouble. My opinion is they’re insolvent. Anyone else who had financials look like this would have declared bankruptcy a long time ago.”

Lapciuc acknowledges that the discrepancy between assets and liabilities is a problem, but the $45 million shortfall in 2012 is considerably better than the $112 million assets discrepancy in fiscal 2011. “Although we’re not in a healthy status, we seem to be on the mend,” he said.

Part of that mending has come with improvements in the economy. Duane Fitch, a Chicago hospital consultant who advises Jackson’s unions, points out that the increase in local tax revenue last year was $8.6 million — more than the audited surplus.

Fitch wonders how much longer that local tax revenue — in property taxes and a half-penny sales tax — will be available for Jackson. It amounted to $335 million last year, while Jackson provides services to fewer patients: In the past four years, in-patient admissions have dropped 21 percent.