If you go to the Archive page, you can "stash" the database for later viewing. The microsd card can hold hundreds of them, although I've never tested the performance with more than a dozen or so.
If you don't use the archive, then HeaterMeter will try to restore the current database from the backup which can hold up to 24 hours of data. However, this relies on the time on the device being accurate when the check is done. If it has an accurate clock (which requires network access at boot time) then it should still be able to use the backup. I'm not sure if the time zone setting can mess with this, but the HeaterMeter should always be set to UTC time zone, since the times are adjusted in the browser. Also be sure your scale on the graph is set to Auto or 24 hours to be able to see it all.