Whether 40s or 4 minutes is the right time doesn't matter. You can re-fix the film in an icecream container or something, it doesn't need to be on a reel or in the dark. If it's underfixed then it will degrade in the long term but there will be no damage at all just yet. It's also very difficult to damage film by overfixing, it takes about 10 minutes before any damage is measurable (yet invisible) and something like half an hour before the image quality is visibly reduced.
So there is a good chance you can save your film now by fixing it longer, there is little to no chance of the film being damaged yet by under fixing and there is basically no chance that you will damage it be refixing, just make sure that the corner of one piece of film cannot come into contact with another piece, i.e. do one piece at a time.