After a long bath or a thorough cleaning, your nails are soft and brittle from exposure to water. How come?
Answer: Nails are made up of small cells, which are mainly made up of keratin. If you examine your nails under a microscope, they look like they are made up of layers in the shape of roof tiles. Nails are very fragile. Your nails can absorb a lot of moisture between the built up loose cells. They even absorb ten times as much moisture as your skin. That's why your nails become so soft and pliable after bathing for a while.
Unfortunately, there's nothing you can do about it, except don't bathe too long and wear gloves when you clean or do the dishes.
Read more about nails.