I don't think design patterns went out of fashion. I think the opposite happened -- they gained such mindshare that they became a solution looking for a problem for many people. That is, they forgot that design patterns are meant to solve problems, and that you should also only solve problems that actually exist. Instead we started getting things that resembled "Hello World Enterprise Edition" [0], which has been dubbed "lasagna code" -- lots of layers with a little bit of filling in each one.
The person I replied to, sideshowb, explicitly asked about both design patterns and Design Patterns. Regardless, that book was what elevated design patterns into common knowledge within the object-oriented world. Their fate is tied together; the book and the patterns described within are practically synonymous.
[0] https://gist.github.com/lolzballs/2152bc0f31ee0286b722