When did freud fall out of favor?

Not really out. Once, the only psychological treatment was psychoanalysis. Many of freud's students then formed their own approaches, some prominent today (jung) others long gone (rank). But out of the original psychoanalytic movement emerged most of the psychological therapies we know today, in addition to psychoanalysis proper. So classical freudian treatment slowly became a minority approach.
Freud's alive & well. It appears that cognitive-behavioral therapy is the treatment approach of choice for many psychotherapists. According to a professional endorsement study by norcross & karpiaka (2012), in 2010, the cognitive orientation was most popular (31%), followed by eclecticism/integration (22%). But, the third most popular approach was psychodynamic at 18%. So, contrary to popular belief freud is not dead.
Still honored. For all his wild imagination, lack of scientific rigor, and unhealthy focus on the inner life and the past rather than outward behavior and the future, freud taught the rest of us doctors that people could benefit from talking and trying to understand themselves, discovering and changing self-destructive beliefs and behaviors. Two cheers for him, even today.
Freud. Not entirely out of favor, as we would not be where we are now without him. However, in the 60's, aaron t. Beck, md and his group discovered that, in opposition to freud, thoughts, not feelings, could produce psychological changes in people and successfully treat depression and anxiety. Beck's work in cbt is the most widely used therapeutic technique today.