Hi Victoria,
Are you aware that you can switch the home mode if you tap the buttons below the list of cameras? (i.e. There's a happy face icon which is "normal" operation and a "home" icon which is for home mode.) I think you are aware of these because you mentioned manually switching back to normal operation.
Is it possible that you tapped the home icon while you were online and caused it to switch to home mode in the first place? If you did that, you did it a few minutes before the camera offline alert occurs, because there's a delay of a few minutes before a camera is marked offline.
Also, I think you have turned off the mode switch alerts. (They're in the home mode settings -- the checkbox that specifies whether or not to send email when the home mode changes.) If you turn them on it should tell you why the home mode is switching. I suspect it's not related to your phones.