You've got several problems with old magnetic media:
1. demagnetization
2. oxide flaking off
3. mould
The first will happen gradually. You can prolong data integrity by keeping floppies away from strong magnetic sources. It will happen eventually though anyway (I believe) due to the effects of the Earth's magnetic field (although extremely slowly).
The second will happen due to age. The adhesive holding the oxide or magnetic coating on the Mylar disc will break down and cause the oxide to powder or flake off. This is called "shedding". Often this oxide will end up on the head of your disc drive, bunging it up. Not much you can do about this...and every brand of floppies will behave differently. Some will still be great and others will be in terrible shape. When reel-to-reel enthusiasts need to rescue shelling audio tape sometimes they will do a controlled bake in an oven to reactivate the adhesive. I'm not sure if this would work with floppies, but you'd have to take the actual Mylar disc out of the hard sleeve to to it anyway. If you try to re-write data to "refresh" an old disk which is shedding oxide, you'll probably end up with a worse problem (as every time the drive head touches the disc surface it will do more damage).
The third will happen if you give mould a chance to grow. If you store your discs in a humid, warm place you'll get cloudy spots on the disc surface. Might look like mottling, specks or even white powder. You can help avoid this by keeping the discs in a dry place. Light won't damage magnetic media (unless it also generates heat) but it can totally destroy burned CD-Rs and DVD-Rs over time). If you've got mould growing on your discs, you might hear them squeaking when you use them (this can also mean the lubricant is gone). Some people have had luck gently washing the Mylar disc (removed from the hard shell) with low water content isopropyl alcohol to wash away the mould, but then the disk should really be archived to another medium and thrown away.
That said...I did exactly what you did (backup my disc collection to ADFs) around 2005. I put all the disks in a non-climate controlled garage loft, except a pack of Workbench disks which I kept in a cool, dark place.
Years later I went to use the Workbench disks and almost all had read/write errors. I had to go out to the garage to get a backup set of Workbench disks and that set worked just fine.
