Goldenberry Storage Conditions
I used to grow them years ago so I could have some summer fruit in an area with little fruit other than strawberries (that I also grew) and crab apples in an empty yard. I had hoped to grow enough to make jam and pies but we ended up eating the fresh. The nearest grocery store with fresh produce was over 1 1/2 hours away.

Since you grow them, you'll know they're similar to tiny tomatoes but their skin is very thin. I've found that with soft fruits (vegetables which are technically fruit too), the thinner their skin, the less keeping quality they have. I left our ground cherries on a large shallow bowl on the kitchen counter and never refrigerated them. They were never heaped in a pile the way grapes are naturally since they were soft. 

I can't see why they couldn't be refrigerated for a few days (2 or 3 only). But I can see a couple of drawbacks that might increase the chances of them rotting though. 


Did you wash them first? 
Generally softer fruits/vegetables shouldn't be washed until you're ready to eat them. Most already have some natural waxes or such (?) on their skin to protect from fungi.  Mind you, I always wash grapes I buy from the store to remove dirt and possible/likely pesticides. But they're thoroughly rinsed after and then laid on a towel for a couple of hours til completely dry. They last much longer that way for me.
Did you put them in a container where they'd be 4 or more layers thick?
The weight of the top layers could easily have broken the skin or crushed the bottom layers. Even a small break or bruise would be enough to start decay, especially if any already had a small unnoticed break. 


If your ground cherries are yielding lots, faster than you can eat them, you could try drying them instead. There are videos on YouTube showing how to as well as multiple blogs and different sites explainin. I had no idea ground cherries were now so popular. I grew them simply to have fresh fruit.