A second day in a row of talks between negotiators for Allina Health and 4,800 of its hospital nurses adjourned Wedneday night with no agreement, as the ongoing nursing strike approaches the state record 38-day walkout by nurses back in 1984.

Allina nurses have been striking at five hospitals since Labor Day, but also conducted a one-week strike in June, bringing their total days off the job this year to 31 and counting.

The progress of the federally mediated talks is unclear, as hospital and union negotiators were not available to provide an update. But the two sides will resume Thursday morning.

Allina executives since February have sought to phase out four union-backed health insurance plans that they viewed as too costly to maintain, and to move nurses to their corporate health plans. Nurses resisted but eventually agreed to that demand in talks just before Labor Day. They then went on strike when Allina declined to give the union requested control over the future cost and quality of those corporate plans.

Talks resumed on Tuesday at the same time as several hundred nurses blocked traffic in downtown Minneapolis outside a hotel where General Mills held its annual meeting. Allina’s board chairman is a General Mills executive.

Striking nurses gained a celebrity boost Tuesday afternoon when those working temporarily at the Ryder Cup in Chaska passed along pins that singer Huey Lewis and actor Bill Murray wore during their golf round.

The prolonged strike is taking a toll. Allina’s cost for replacement nurses during the two strikes this year easily has surpassed $40 million. Striking nurses are scrambling to find replacement income and appealing to the union for hardship funding.