Cold brewed coffee does not contain some of the coffee oils that hot brewed coffee does so it doesn’t oxidize or grow rancid as quickly.  Note: oxidation and rancidity refer to oils developing an off taste and is not the same as the microbial growth discussed earlier in this post. Personally, I would keep cold brew in the fridge for up to a week. In my house, a batch rarely lasts that long.  The best taste is usually in the first 2-3 days, then I start to notice a deterioration in flavor.