Hi Heidy, if your starter is routinely doubling within 6-8 hours after a feeding, then it's perfectly safe to store it in the refrigerator. This will not harm your starter at all! We recommend feeding your starter at least once a week when you have it stored in the refrigerator: just give it a feeding, let it sit out at room temperature for 2-4 hours to start bubbling, and then store in the refrigerator for up to a week. When you want to bake bread, you can generally feed the starter right out of the fridge. Look for it to double within 6-8 hours as a good sign that it's ready to leaven your bread. Your starter will last much longer than a week in the fridge, but the longer it's been since its last feeding, the more room temperature feedings it will likely take to restore it to its normal rising behavior. 

• Reply