No, the database does not update once per day. The database updates as soon as it can (which is why the FTF list page is current). "As soon as it can", however, still means that you need to allow 24-36 hours from posting the online log before the log has been detected and processed so that it is available in the database.
Once information is in the database it can be seen by the pages on the site. The FTF list page (and, indeed, almost all pages) use information live as soon as it appears. The Profile Statistics page is different, though, since it takes a very long time to generate. If you request this page and it has been generated less than 24 hours ago, then it will show you a cached version of the page generated earlier (assuming you are a paying member of Project-GC, otherwise it uses the same page copy for a week). Once the page copy is more than 24 hours old, a new request for it will cause a new one to be created.
As you can see, 32 hours is well within the expected timeframe.