Retailers all have the right to discount your book if they choose. You can rest assured a retailer's discount for your print edition book will not cut into your proceeds. When a retailer discounts a book, they are the ones eating the cost of the price reduction. In other words, your earnings will still be based on the original retail price.
Retailers can discount a book for less than the lowest retail price they allow us, as the publisher, to set. They are making the decision to accept any loss by covering necessary production costs on their end to bolster sales for a title. If a retailer discounts your book, this can be a great promotional tool to advertise to potential customers that your book is on sale.
The one exception to this is if Amazon decides to discount your eBook in order to match a lower price it finds elsewhere. In this case, your eBook earnings will be based on the discounted price as eBook prices are required to match across all retailers.