Thank you for your post. The issue you are experiencing may be due to many different reasons. some things to look at would be the DNS setup of the domain. Another option would be to look at the forwarding and inbox rules for your address. If the email is connected to an email client such as outlook or apple mail, these programs may have other external rules that are routing the mail improperly.
With Office 365 there is an option to preform a mail trace for incoming and outgoing emails. If an incoming message is marked as 'delivered' in the mail trace but does not display in the inbox, the trace will in most cases show where the mail was routed to, be it a separate folder or address.
If you would like assistance in reviewing your Office 365 basic setup please feel free to contact our customer support line and they will be happy to review with you.