I haven't been fly fishing very long, but I'll say over the past year, I've had it happen twice. Once was nymphing in a deep slow pool, and I just never detected the strike. The other time was a dry fly that got inhaled and I had too much slack in my line, and by the time I set the hook, it was back a little farther than I'd have liked.

Luckily, in both cases, the hook never really set deep. I was able to just turn the hook at a slight angle and the fly slid right out.