Hi there,
I've been running mavericks and outlook 2011 for ages with office 365 fine (had it off the developer portal pre release).
Can you describe your environment a little better please.
Are you federated? dirSync? Kerberos authentication?
I would suggest to start you check formal, updates see if anything is available for mavericks and office.
Create a new identity but holding down alt as you open
Hit the + button type testidentity or similar then right click and set as default.
Once done close he database utility and reopen outlook
Set it up again as a user and see if the problem persists.
Graham