During my years as a seller of vintage clothing, I've run into this label a few times, but I can never find any information about this designer or design house. All of the garments I've had by Rappi have been from the 50's and 60's, and all but one were cocktail or evening dresses.
So, I'm sending out a plea to the vintage community. If anyone knows anything about Rappi, please comment here or contact me through the website.
UPDATE: You'll find some great information about Rappi in the comments. This photo of her comes from a vintage sewing pattern.