Hay isn't going to go stale in a couple days, however, rabbits seem to prefer it when it is first placed in their cage. They will often begin to ignore hay that has sat around in their cage for half a day even. Of course the hay in the bale (or bag) isn't any different, but there is something about placing it fresh in their cage that entices them to eat more -- which is great!
A bale of hay (that's how I buy my hay) can last for many months provided it is kept out of the sun and moisture. Otherwise hay can get either dusty or moldy.
Don't wait for hay in the cage to be gone before refreshing it. Expect wasted hay. They like to pick through it for their choice pieces. Add new hay every day (or twice or more per day).