Kristin, I’ll give my experience here which will differ from most others so I hope post their experiences as well.
I have never run deals on Prime day or other big days like Cyber monday etc. I think your approach should always fit with what happens in your niche, what your goals are and how you want to run your business.
I’ve been in the fortunate position where I haven’t needed to run discounted promotions or deals to maintain my rank so I don’t necessarily like reducing my profit margin just because there is a special event.
I find that on Amazon that the rising tide lifts all boats. On previous Prime Days, my sales were 300% of my usual daily sales without doing anything (in fact, sometimes I’ve raised my price as people are just in the buying mood.)
Perhaps I could have got more sales and more net profit if I’d run deals but I’ve always been happy with riding the rising tide.
PS. I don’t remember sales ever reducing in the days leading up to Prime Day