From the thread "Royal Icing Decorations on cake question", I wrote:
Yes, grease-free utensils while you're making it, but it doesn't have to be a grease-free surface that you pipe it directly onto, nor completely dried to stop it from breaking down. (moisture is the culprit.)
There's a similar thread from a few days ago that discusses what causes royal icing to break down titled "Deciding between fondant, icing, gumpaste, and buttercream". I'll paste what I wrote below...
Here's the entire thread:
http://cakecentral.com/cake-de.....html+icing
...you can apparently make royal and pipe it directly onto Crisco greased forms and pipe into cooking-sprayed foil-lined lily nails!)
If you'd like to read what others have experienced, TexasSugar says that it's caused by moisture in this thread "question about royal icing":
http://cakecentral.com/cake-de.....html+icing
and here "Royal icing decorations":
http://cakecentral.com/cake-de.....html+icing
my favorite "will piping gel break down royal icing":
http://cakecentral.com/cake-de.....html+icing
another favorite, "Royal Icing Lilies, Cooking Spray...":
http://cakecentral.com/cake-de.....html+icing