I understand how the way the original comment phrased things sounded, to your ears, like "at least 24 hours should pass between reboots," which is not what was

I understand how the way the original comment phrased things sounded, to your ears, like "at least 24 hours should pass between reboots," which is not what was intended. And your suggestion, "at least once every 24 hours," would be perfectly acceptable and idiomatic English. However, "at least every 24 hours" is also perfectly acceptable and idiomatic English. It is very common in English to use this construction, "at least every X time period," to mean "X often or more often." If you say, "I make sure to call my distant relatives at least every year," you mean with that frequency or more. If you say, "I make sure to stand up and stretch at least every hour," you mean with that frequency or more. If you say, "these machines are required to reboot at least every 24 hours," you mean with that frequency or more. In other words, "at least" does not qualify the number of hours (such that more hours would also be acceptable), but the frequency (such that greater frequency would also be acceptable). Hopefully this response helps you to understand why English, fickle language that it is, works this way in this case.