According to the Wilton school of home cake decorating, the "American" buttercream recipe calls for 1 cup fat to 4 cups 10X sugar. Of course there are a million different ways to "tweak" it, but theirs is the one that has been used by home bakers for generations,will never fail and is tried and true.
How long and at what speed are you beating the product?
Too much air will create a overly fluffy product that is beautiful while cold but will rapidly lose shape when coming to room temp.
Same if the room is really humid or hot.
Butter has a low melt point and will quickly lose shape in an overly warm room.
Sugar will draw moisture from the air and "melt" the icing.
My suggestions are
1. Use an all vegetable shortening instead of butter. Before you say EW! Gross! Consider this, almost every bakery and professional decorator will use all veg shortening or super pure lard in their BC recipe. This is how they make such a beautifully smooth final product and piping that that will hold shape for days.
2. Add a few tablespoons of meringue powder or more 10X to your recipe. Both will help your icing "crust" and retain shape.
3. Follow your recipe religiously when mixing. Too fast or too long will make things nice and fluffy, but won't stand up when all that air is released from the product.
4. If at all possible (meaning there are no high risk ingredients in the cake) don't refrigerate the iced cake. The sugar in the icing will pull the humidity from the fridge, leaving you with a too soft product that won't hold up.
My, aren't I long winded today? This is what you get when I have insomnia! Good luck with the cake (IMHO parents should always make their childrens bday cakes!) and Happy Birthday to the lucky child that has parents who care enough to give the best gift of all. Their time!