The floppy can "go bad". If so, you are out of luck.
The heads on the drive can eventually become mis-alligned where they can not longer read thedata.
The headscan become dirty. Result is as above.
If the problem is the drive, go get a used one for $5-10.
If the floppy is bad, then use another floppy.
One can always compress the files and mail them to yourself.
Or get a USB memory stick and put the files on it to move them across to another system.
Unless you can remove dust that is inside the floppy dirve AND that is the problem, you will need to invest some time and shoe leather intoresolving the problem.