Once in a great while I am asked to log in via my iPhone:
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<span style="font-family: 'courier new', courier;">I honestly haven't paid enough attention to when or why I get logged out. I do not get logged out that often. The theory of having to log in when switched networks is something I will have to pay attention to though I don't think so in my case. I switch on and off of a few different wifi networks in the course of a day (house has one, cars each have one and my home computer uses an ethernet connection) and I don't have to log in often enough for it to be that. Now that I think about it I don't remember the last time I had to login from my computer that uses ethernet. My phone and iPad do logoff from time to time.</span>
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<span style="font-family: 'courier new', courier;">I use pretty much apple products across the board (iPhone, iPad and MAC computer). I don't know if that matters or not. I notice that on all my devices I occasionally have to log in and other times it is still logged in from the last session. I do have the login saved in my Keychain. When I do have to log in it will autofill my credentials. Not sure if that has anything to do with it either but I don't think it would. All the autofill does is populate the fields I still have to click the login button. </span>
<span style="font-family: 'courier new', courier;">I guess that's a long winded way of saying mine is so random it's hard to say what causes it.</span>