At what point should carrots be thrown away?
If your carrots are going soft after just a few days, you're not storing them properly. Mine keep for weeks and weeks. I leave them in the plastic bag, and keep that in one of the vegetable drawers in my fridge. How are you storing yours?

A rubbery soft carrot isn't bad for you, it just isn't very pleasant. A slimy carrot is bad for you, don't eat it.