It's not technically "fatigue" in the metallurgical sense since you never ever really stress a frame close enough to its yield-strength to do work-hardening anyway. I suspect what happens is that the tubing themselves are fine, but you end up with lugs and brass that ends up with microscopic cracks. I've cut apart old steel frames and have found a lot of corrosion in the lugged joint itself where there once was full-contact with brass.
So yeah, old steel frames do get softer from A LOT of empirical evidence. However, HOW that softness develops is arguable and certainly is not metal "fatigue". "Frame fatigue" is a more accurate way to describe it perhaps.