HC-110 seems to be in the Rodinal department as far as shelf life.
As soon as you dilute it with water, it oxidizes more quickly, however. Even so, I've had 8 month old stock solution work perfectly for Delta 3200 at 4000 (a two stop push from the film's actual speed of 1000) when stored in a half full 8 oz. amber glass bottle. If it worked perfectly after 8 months, who know how long it would remain usable as a stock solution, especially in a full bottle?
I usually mix up small batches of stock solution, instead of the whole bottle, just to be safe. But I would not worry about shelf life with HC-110. Just take some precautions, like decanting the syrup and stock if the bottle is at or below the halfway mark.