I'm a little reticent to answer this since the last time I answered a question about how long I kept something, I was informed how wrong I was to do so. But, since I hate to see you go unanswered, here goes:
I, personally, have frozen royal icing for over three months and used it after thawing with no problems. I don't know about leaving it on the counter more than a week as I haven't done that. Hopefully, someone who has will come along to help.
From what I've read, royal icing can stay out for 2 weeks in a airtight container. I make a large 4 pound batch and put in small individual containers. I keep one out and freeze the rest. I usually get through this small container for my week's cakes. If you color the icing, just freeze it for future use.
I had no idea you could freeze royal icing! I love learning new things!! 
Oh yeah! I don't use royal icing much, so I make a batch and freeze what I do not use. I just defrost it, use what I need and pop the unused stuff back in the freezer! I freeze leftover everything!! The worst that will happen is I will have to throw it out! Usually, I am surprised at how well things freeze if wrapped very well!!
I keep for up to 2 weeks - this is of course RI made with meriwhite and not fresh egg whites after that I either ditch it or, a fab useage for old stuff, is to make pastillage out of it. You can make hard structures, support sticks etc out of it. i use it for castle turrets etc HTH
If it is made with fresh egg whites, it will only last a day, after that the texture isn't the same. If you aren't fussd about the texture, it will keep for 2/3 days. If it's made out of meringue powder, I have kept it on the shelf for up to 2 weeks before throwing out. But I have never heard of freezing it! Will definitely give it a try.
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