I work at a mid sized Amazon 3rd party seller. We reprice automatically. With thousands of SKU's there's no other way to be competitive. There are many layers to consider though, you definitely can't let your whole catalog auto-reprice. Usually sellers just focus on their top X% SKU's and let the rest auto-calculate.
I wonder if we have a price ceiling setup...?
Edit: Yes we have a floor and ceiling. I have no idea what I was thinking.