How long should boiled water used for powdered baby formula stay in a Teflon pot? Can it stay in the pot for days?
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.
Rumtscho's answer is close to right but wrong enough that I feel I need to post this.
You need to bring the water that you use for formula to a boil before each batch when using powdered formula. This is important because you kill any possible bacteria in the water AND it provides hot enough water to kill any bacteria that has found it's way into the powdered mix. The powder formulas are packed sterile, but once you open the sealed package, the air could introduce pathogens.
You should only prepare one serving at a time. Prepared formula is a perfect growth medium, therefore you need to minimize the time it sits around. You should make sure that you are cooling the bottle with either running or iced water, but making sure to dry the bottle and making sure that the unboiled water doesn't touch the ring or nipple. If you have to prepare formula that isn't going to be used immediately, make sure to cool and then refrigerate. NEVER SERVE YOUR BABY LEFTOVER FORMULA!
You can use the same water in the pot for multiple boilings. Each boiling will kill off anything in the water. However, you do need to make sure that the pot remains covered between boilings, as physical or chemical contaminants could remain in the water after boiling if they manage to get in the pot.
Here is an additional source that is laid out well. All of the stuff in this, and the source are basic food safety. It just becomes extra important because you are feeding a not-yet-formed immune system a perfectly formulated growth medium.