Or quit using floppies
But if you really must use them, yeah, replace the drive.
I wouldn't advise keeping anything important on them. Compared to what's available now, a floppy disk is just about the most unreliable storage medium. Sensitive to just about everything (heat, magnets, water, stress), they are easily damaged.
Consider converting what you can to CDs or other more reliable storage. If you require editing of the files, a flash drive would be ideal.