The general answer I see on here is that there is enough sugar in frosting that it preserves the dairy in the recipe. I make my frosting with half butter and half shortening, and use heavy cream in it, and it's been stored in a sealed container on the counter for more then 2 weeks without a problem. In culinary my chef has us make frosting with egg whites and we had buckets of it that we left at room temp, I thought he was crazy (and he was old-school) but we never had a problem with it. I think it depends on what you're comfortable with, but I wouldn't stress over it. Also, lots of people leave butter on the counter so it's soft for toast/etc without problems.
Sugar in high concentration creates an environment of low water volume so when a microorganism is introduced, the fluid within it's membrane will want to transfer to the outside environment. So pretty much the microorganism becomes dehydrated and dies.
I've read articles where veterinarians have used sugar in infected or large wounds caused by motor vehicle accidents. Not saying this is the go-to treatment, but it can be used.
I hope that helped and I didn't give you too much info. 
I am a bit of a fraidy cat about butter but I use a 50/50 mix and have left it out for 2 days with no problem. Klutzy_Baker is right about the sugar. It works the same way salt does as a preservative on meat.
That being said, I still try to keep it cold when I can. Can't hurt, right?
I have had frosting with butter out on brownies for a week with no issues. I keep my BC in the fridge in between when I am going to use it again. But once it has been put on something I have never refrigerated the cake/brownies out of concern for the butter. But then again I am one of those people who keep butter out on my counter so it is soft for bread/toast and have never had any issues.
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