The nation’s six-year streak of declining coal mine deaths came to an end in June, when 32-year-old Marius Shepherd was thrown from a runaway locomotive steaming down a mineshaft in Hueytown, Ala.

Five more miners have died since then, bringing the 2017 total to 14. Worker advocates fear the death toll could rise even higher in future years, although mining companies say the current safety rules are working well.

“It’s not broken,” Henry Chajet, an industry attorney with...