I have used the no fail recipe without any problems and the cookies come out nice and crispy. I have been decorating them using fondant but last week I decided to flood them using royal icing.
It worked really well but as I left them to dry, the royal icing dried beautifully but the cookies themselves ended up very soft and were not at all crispy. I had to leave them to dry for 3 days but I think by then, they would not have been edible.
How do I stop the royal icing moisture going into the cookies?

I have no idea as I made my first batch last night and will be icing tonight. I also would like to know so here is a bump.

Letting them sit in the air for that length of time will soften the cookies.

You could be using too much icing in your flooding. Royal should dry overnight. The cookie will definitely steal moisture from the icing.