Kodak HC-110 and Ilford Ilfotech HC are mixed in ethylene glycol (if I remember correctly), no water, so that they are rather impermeable to oxygen. This leaves the syrup with enormous shelf life.
However, I've been very happy with the shelf-life of open bottles of Ilford Ilfotec DD-X. Have almost always gotten a year with no problem in by cool basement. I did have a crystallization event in one bottle that had about 20% left in a cold winter, had to ditch that. But I've never had it fail, and never felt that old DD-X was giving me under-developed negatives. I like everything about DD-X except the price. (You won't catch me mixing 36 ounces of it to feed my 4x5 Nikor tank.)