I think how you air dry relaxed hair makes the difference. If your hair isn't thoroughly moisturized or if there is a lot of heat on in your house at the time (from a radiator or oven etc) and also if you put something on over the braids.
When I did a braid out, I moisturized the hair and my scalp a lot and then I covered my hair with both a scarf and a satin cap. I also used rollers on my ends and I think that's why my hair was the most moisturized it's ever been.
Even my mother said, your hair is soohhh soft. It stayed like that until I washed it again, without applying more moisturizer.