Taken from this reddit thread; https://www.reddit.com/r/ffxiv/comme..._getting_sent/

Tldr if you own a house and haven't been in it for a while, you may or may not be receiving the proper warning emails about the demo timer (for a variety of possible reasons). Apparently this seems to have been going for a few months now but I never saw a thread about it here on GD so I thought i'd spread the awareness. And if its been posted before, well, a reminder doesn't hurt I guess. Double check the timers on your houses, and remember it only resets if you step inside the house itself.