wow, ran into the same problem today and that was chilling... wouldn't want to lose the save...
I looked at the source what this mod does and got some hints; it seems when you go to the mod settings (after loading the save that's running slooooowwwww), in map tab at Break Time and change either Break interval or Break Duration, it seems to reset the time, speed up the game to the original 60FPS and everything seems to run fine... I don't completely understand why that is, but this seems to be the effect.
I just tried this and will have to find out how it behaves in the next hours and after saving, but maybe that's the workaround.
Maybe the mod should initialize the timer and speeding up to 60FPS when loading a save, doesn't seem reasonable that you're stuck in your break. I reckon that could also happen when autosaving, which would render the purpose of autosave unusable if you're stuck in the slow zone and need to restart from an autosave...
edit: mmmmh, might be tricky, though... https://forums.factorio.com/viewtopic.php?t=103250
or maybe force a save right before the break hits? that's actually what you really would want to do, if you choose to call it a day. Something like the auto save that happens when you start travelling to a planet the first time, although I don't know if a mod can trigger this or if it's hard coded into Factorio...
edit2: maybe https://lua-api.factorio.com/latest/classes/LuaGameScript.html#auto_save
so, maybe in the line before https://github.com/Identifier/FactorioMods/blob/78b37d17c1cad857823227067a55f6f4f4053a7e/BreakTime/control.lua#L52
add
game.auto_save("BreakTime_before_break")
might result in an _autosave-BreakTime_before_break save file, if I'm reading this right...