Hands down, my most reliable have been from private, reputable breeders who don't have stock that originates from hatcheries. If my birds around here die mysteriously, get sick, get egg bound, or aren't as cold hardy as said to be - They're my hatchery girls.
Otherwise, the hardiest of mine are my Araucanas. Tough buggers who are also good moms, quite broody, and very good egg layers. Also their lack of tail allows a lower chance of getting caught by a predator.
I also find that gamefowl (american or oriental) are very hardy, but only in warm or hot climates. Plus males do not do well together.
A good breed for a general backyard laying hen is an Ameraucana. (I mean the purebred type, not the Easter Egger type) I've never ever lost any to sickness or predators, never had any that were mean, they aren't as broody as Araucanas (a plus for people who just want eggs) they're very calm and sweet, and lay beautiful eggs. Plus they can come in some very beautiful colors like Blue Wheaten, Splash, Buff, and Lavender.
The only drawback is finding rare colors (if you want rare colors) if you don't want to hatch your own eggs (which I personally prefer though) and finding local breeders who have real Ameraucanas, not Easter Eggers.
