Check through your OE message rules to make sure that you don't have one that dumps his emails somewhere else.
If that's not the case, go to your provider's web site email section and see if the messages are actually arriving in your inbox. It may be that your provider is filtering these out. If there's a spam box there, take a look in it. If that's where your contact's emails are going, open one and select "not spam". That should correct the problem. You can then move all the dumped emails to the inbox and they should then get downloaded next time OE checks for new mail.