Hi Will,
According to the log you have added, I suppose you are using Office 365 pre-upgrade for enterprise and I have done the following test:
1) Open Outlook Web App.
2) Click sign out button.
3) I will get to sign in page and it will not sign into Outlook Web App again automatically.
I’d like to confirm when you say “the session logs out, and then immediately logs right back in”, do you mean after you sign out Outlook Web App, it sign into Outlook Web App automatically without typing in any Office 365 credential?
If yes, since this issue doesn’t happen to me, to narrow down this issue, please try clearing cache and reset IE to see if there is any improvement.
If the issue persists, I’d like to confirm the following information:
1.Does issue happen to all the users in your organization or just your account?
2.Which browsers have you tried to reproduce this issue?
Thanks,
Vivian Wang