Boiled water left in a Teflon pot
Water is not infinitely shelf-stable. No matter what you store it in, it keeps for a short time. The Brita instructions for their water filters say 1-2 days, and this sounds reasonable to me for normal use. 

But because you are asking specifically about baby food, I would recommend to not let it stay at all. The reason why you are supposed to boil water for baby food is to kill any bacteria present in it. The moment the water's temperature falls to survivable temperatures, bacteria from the environment can start colonizing it. So if you let water stay around after boiling for a few hours, it will be as dangerous as water which has never been boiled. If you let it sit for longer, it becomes much more dangerous than just using tap water without boiling. 

Bottom line: Boil the water fresh for each batch of formula, and use it as soon as it has cooled down to baby-acceptable temperature. If you leave boiled water stay around, it is worse than not bottling it at all.