Hi Kari, it's perfectly fine to put your starter in the fridge a few hours after you've fed it. This is actually a better approach than putting it right in the fridge after a feeding, since sometimes this can cause fermentation to shut down too quickly. When you're feeding your starter at room temperature, ideally you do want to feed the starter when it's still in the ripe zone (at its peak rise, or just beginning to fall). Feeding the starter when it's still ripe helps to keep the yeast more active and vigorous. However, it's certainly not going to do any permanent damage to your starter if it falls now and then, and we never recommend getting up in the middle of the night to feed your starter! 

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