Hello @lizbonney,
Thanks for writing in and sorry to hear that you’re still having this issue.
Did you happen to try switching to another theme for a while to see if the problem persists as @Prasant mentioned? If it’s possible for you to do so for a couple days, that could help to narrow things down that it is indeed not happening due to the theme and is instead some type of hosting issue. If you have not done this, I would recommend doing this to see if the posts still reappear when another theme has been used for a couple days.
Also, regarding the posts that keep reappearing: are they specifically X Demo Content, or are they old posts of yours that you recognize?
All that being said, even if the posts are X Demo Content, because of the nature of this problem (and the fact that I have not heard this reported by anyone else), I am inclined to believe that this is likely a matter you will need to take up with your host. Perhaps you have some type of backup system in place that is erroneously triggering each day, causing the issue to persist. At this time I would personally recommend contacting your host to see if they can help you with this or shed anymore insight on things, as this will most likely be something for them to fix on their end. After consulting and working with them, if they cannot seem to locate the source of the issue and you have tried switching themes for a couple days to see if the problem persists with another theme, let us know and we can continue to look into this.
P.S. As @Prasant also mentioned, do you have any type of backup plugin installed on your site that might be misconfigured? That would also be something to look into as well with your host.