IMO it depends of what sort of disaster your talking about, the particular type of disruptions involved and how much damage is inflicted.

Generally I have observed that national retailers tend to close as soon as they lose power external power. Plus or minus how long any backup power is designed to last. Some or these stores keep selling as long as the backup generator keeps running and the cash registers keep working. Other close as soon as the main POCO, power company, electrical feed fails. At least one grocery store manager said they close the store to sales even if the emergency generator is running so they can make the reserve fuel last as long as possible. Shutting off interior lights, ventilation and other non-essential loads and reserving the generator for powering the refrigeration so the food doesn't spoil.

Smaller mom-and-pop retailers are much more likely to be free of advanced stock controls, computer scanners and integrated registers. Most can operate quite well with cash only sales. Usually if the power is out credit card sales are impossible so cash is king. It has been my experience that they also are far more motivated by connections to the community and dedication to their family store to stay open as long as possible to protect it and cater to their customers.

During the LA riots family owned stores were often manned, protected and were the last to close and first to reopen. Big-box stores were largely abandoned and how and when they reopened was a corporate decision.

Of course all retailers will have problems maintaining staff. In an emergency the employees want to go home and tend to their families. Major retailers need a good number of people to operate. A small store might get by with a one or two people. Sears or WalMart might need a dozen or more. Even if they get power back they aren't likely to open until they get the manpower to run the store.

Of course if there is massive damage from winds or flooding the stores can't be expected to stay open or to reopen until they can be repaired, cleaned and restocked. In a case like NOLA the store contents of national retail stores are listed by insurance as a total loss. In this context looting might be taken as independent salvage. There is no way any major grocery store or retailed is going to go to the trouble of sorting and sifting through a flooded or severely damaged store. The typical recovery plan is that the entirety of the store contents, including the shelving, are loaded onto dump trucks and hauled off to the landfill.

You have to realize that the replacement cost of retail goods is usually 10 to 50% of the retail cost. It doesn't pay to do much detailed salvage and reconditioning in the hopes of selling the items. Labor costs and insurance liability make it impossible to make a profit. So when you see 'looters' coming out of a flooded shop you might consider it just one less thing the owner will have to load onto a truck and haul to the dump.

For a flooded store, without structural damage, reopening would be a week at an absolute minimum and a couple of months likely. It can be expected that some badly damaged stores may not ever reopen.

So the answer to ther original question when will stores reopen is they will reopen, at the soonest, when they get power and have the manpower to run the operation. This assumes there is no major damage and, for food, the power wasn't off long enough for a significant portion of the food to go bad.

Clothing and dry-goods stores usually don't have back-up generators. Food stores usually do. But typically these systems are only designed and fueled to operate for 72 hours or less. One store manager claimed his was set up for 48 hours but could go for a week or more if they could get fuel to keep the generators going. After the generator fails he has 6 to 12 hours before the refrigerated food goes bad. Once it does the store is limited to boxes and cans and may not be deemed worth opening until the entire stock can be removed and replaced. Hard to see that happening in less than a week.

Expect reopening to take longer if, as in a hurricane, a wide swath of territory is disrupted with roads out, people displaced and recovery crews and materials in short supply. It has been three years since Katrina and a lot of the smaller towns have lost all or most of their retail stores. Entire neighborhoods in NOLA are still short of any retail space beyond small convenience stores. Of course some poorer sections had little more than convenience stores to start with. The more affluent areas started with more and saw them recover faster.

This isn't a simple answer but perhaps you can take some of this into account when considering your situation. You might also go around to your local retail stores and simply ask the manager. Some stores have disaster plans while others don't. The local store that stayed open was a tiny little convenience store where the manager lived in the back. When the hurricane came he had no place else to go so he hunkered down and stayed open the entire time. You might want to scout out all the local mom-and-pop stores.