Consumers are the ones in control during the holiday season and for the finicky buyers it might take a deal to get them in the door. For retailers, the dilemma of getting buyers into the store with deep discounts and appeasing the investors is a juggling act, but it is essential. No customers equals no sales. Even if the enticement is a deep profit cut, people are more likely to buy other items during their shopping trip.
Yes, retailers should continue to offer deeply discounted prices during the holidays if they lose value in their stocks. By continuing to offer the low prices, they are encouraging sales to close out the year. People will spend the same amount of money and possibly more when they get lower individual prices so it will improve sales overall.
If the retailer believes they are able to profit or otherwise perform well during holiday periods by lowering prices then the value of shares on the stock-market shouldn't be a reason to counter this. Long term value can be found in customer awareness, image or even more profit (higher volume at lower margin).
Stock prices change all the time and are not short-term barometers of success.
No one will buy stuff from them if they do not offer deeply discounted prices. People like their sales, and if they do not want to lost even more money they need to keep those prices low. They would end up losing even more money if they don't keep up tradition