The unit should not shut off on its own. Is it really completely off or just idling?

In the app, the IO button isn't illuminated.

And the device itself? Is there anything displayed?

Omg, I thought my machine was the only one doing this! I have 2 HP07 and the one in my bedroom (where I spend most of time) keeps shutting off randomly.  

Like you, it’s on auto, cool mode, and it runs and then sometime in the evening it shuts off.  I then have to turn it back on (via app or remote).  

My HP07 in my office doesn’t seem to be doing this but I’m not in there daily.  I had restored this machine back to factory settings 2 months back and wondering if I have to do it again.

It is aggravating to say the least as I have dogs and need it to constantly run. I’ve had it for years and it’s always run 24/7 so not sure what’s going on.

A few days ago I posted a response, I don't see it here, so I'll try again.

Anyway. A few times the machine has gone dead dead. The first time it did this, on the app it wouldn't connect and threw up a dialog about some error I don't remember now. At the unit, pressing the power button (even holding it) didn't do anything (display is unilluminated). I unplugged the unit, waited a bit, and plugged it back in. I was able to power it up and talk to it with the app. On subsequent occasions unplugging/plugging has revived the unit. 

I have read in different forums about an undocumented feature where if it's in heating mode it will shut off after 9 hours (for safety). I'd imagine this applies to cooling mode too. Maybe this is what PandaBear is experiencing?

It's been a few days since it's last incident, but if I get any more I'll gonna try the warranty for a replacement. 

I really don't like the info (or lack thereof) that the app provides. I'd like to see a display of actual temp set-point and what mode it's in. Even better have a heat set-point and a cooling set-point. So I could have a band where it just cleans the air. I.e., have heat below 65 deg and cooling above 80 deg.