The whiskey distilleries in Kentucky and Tennessee typically shut down during the hottest summer months. Historically this had a practical purpose as it can be very hard to control fermentation, which produces heat as one of its byproducts, when atmospheric heat and humidity are already high.
With today's modern chiller systems and other process controls it is possible for distilleries to run year round and they more-or-less do, although most still have a shutdown of at least two weeks in August.
The shutdown is a chance to do deferred maintenance and repairs, install new equipment, make changes, and do any other work that can't be done while the distillery is in operation. For some companies shutdown is a good way to handle employee vacations.
It's unfortunate that shutdown typically occurs in August, the busiest season for visitors. As tourism becomes more important to revenue streams, they may change that scheduling. Although in some ways, if you're touring a distillery in August you should be glad it's not operating. It gets hot in there.
Shutdown is also a good way to adjust the distillery's output for the year. If you are a bit overstocked with new make, you can correct that quickly by extending your shutdown by a few days or weeks.
Like most manufacturing enterprises, whiskey makers have gotten good at managing just-in-time supply chains, but that means many other pieces of the supply chain are forced to shut down when the distilleries do.
Cooperages, for example. It's hard to imagine the volume of barrels Independent Stave and Brown-Forman produce. Jack Daniel's, the largest single distillery, fills more than 10,000 barrels (at 53 gallons each) a week. Neither the cooperages nor the distilleries have space for storing thousands of empty barrels. At the distilleries, the cooperage trucks pull up and unload new barrels directly into the filling area. By the time one truck is emptied they're ready for the next one.
So when distilleries stop filling barrels cooperages have to stop making them. Presumably it's like that all the way back to the forest. When the distilleries stop distilling the lumberjacks stop cutting.