Does anyone know if there is an estimate about when the next "Song of Ice and Fire" book is due out?

Answer 1

well looking at the publication dates of the published 4...1997, 2002, 2003, 2006...it's hard to speculate. This will be your best place to check for updates though: http://www.georgerrmartin.com/if-update.html

Answer 2

He hasn't finished the book, and he's not going to say how it's going until he's finished.

So, no, there is no estimate.