No, that's not what happens. They lock in a price when they alert you to the upcoming delivery round.

https://www.amazon.com/gp/help/customer/display.html?nodeId=...

The price of the item may decrease or increase between deliveries, but will never be higher than the price shown in your reminder email.

I sometimes get "item available" cancelations for this reason. The items are always available, just not at that price.