The reason SSDs have limited rewrites is because there's a physical membrane that electrons tunnel through to store bits. This membrane will break down over time as writes are made.
For a more visual representation: Imagine you have a bowl covered with plastic wrap that's upside-down, and you push some BBs through the saran wrap from underneath. At first the BBs will stay in the bowl pretty well, but the more holes you poke in the plastic wrap the more likely they are to fall out. Eventually there's so many holes it can't hold anything.