Okay, so we've shown that you don't need to worry about reboiling water more than twice. It's perfectly safe and will not be hazardous to your health in the short or the long term.

Is kettle boiled water safe to drink?

But scientific advisers called in to study the results warned against coming to conclusions beyond that "boiling water in some types of kettle may result in elevated levels of nickel in the water".

Why should you not Reboil water for tea?

Is there any reason you can't just reboil leftover water? The tea lover's argument is that water contains dissolved gases that contribute to flavor development as tea steeps. Reboiling water depletes the levels of dissolved gases, thus making a less flavorful brew.