I have found the thread below which addresses our issue specifically but it appears this problem was addressed last year...however...we are having the exact same issue in that we have to close and re-open Outlook in order to receive new e-mails or click the update folder button. Anyone else experiencing this? Any fix or suggestions? We are brand new to Office 365 and have followed all guidelines. Thanks!
http://community.office365.com/en-us/forums/160/t/14589.aspx?PageIndex=1