So took a look, and the Devotee algorithm uses the underlying database time, which is UTC (Universal Time, like GMT +0). When you see your post times, it applies the local timezone as needed.
For the badge, if you access the forum in a 24 hour sequence that fits UTC then you’re fine, if you don’t (like you’re in a timezone where you’re +8 hours past UTC) then if you post early morning one day and then late at night the next day then you could miss the entire ‘UTC day’. Mystery solved.
Having said that, if this does happen then let us know in a PM and you’ll get the damn badge anyway, as that seems like a pretty weak technicality for a ‘1 year run’ not to count.