Floppy disks are prone to becoming unreadable for the simplest of reasons. Something as simple as a tiny piece of dust, dirt or hair coming between the disk and the disk reader can cause this problem. They are great for their portablity but it's generally a good idea to keep a backup copy of their contents on some other media, Zip, Flash, hard disk, CD or perhaps even a backup floppy.
You could try just giving the floppy a good shake in hopes this will rid any such debris. If you have a can of compressed air you could try giving it a few shots with that or perhaps just blow on it a few times. Sometimes they go bad because a portion of the magnetic media has become corrupted. This can happen for various reasons. It's also possible the floppy is okay and it's the floppy reader drive on your PC that's going flaky. Try to see if the same floppy can be read from another computer. Over the past several years, computers with floppy readers have become pretty scarce but check around, you may find a friend or public libray or somebody who still has one.