I went off anti-depressants at about 5 months sober. I kept an open mind and was willing to re-start them again if needed. But what I found was that with working a real recovery program and experiencing the results of that, my problem was alcoholism, not depression and anxiety.
It's been a few years and I haven't seen any need for anti-depressants as long as I continue treating my alcoholism. YMMV.