There are loads of different ways or receiving emails. Without some more information your post will remain meaningless to us.
Which device are you using? (Windows PC/laptop? Apple Mac? Android phone/tablet? iPad? Something else?)
How are you accessing your mail? (Do you go to a web page or do you use a dedicated email client/app? If so, which one?)
If you're using a dedicated email client/app, do you know whether your emails are synced via IMAP or are you using a POP3 connection? (Don't worry too much if you can't answer that though. I'll just assume that it's IMAP unless it's obvious that it's not).
If you trawl through the list of emails in your Inbox, are the relevant messages still there (even though they're not showing up in the search facility) or have they completely disappeared?
Does the search facility only fail when seeking messages from your friend or is it completely dead? (i.e. if you search for messages in your Inbox from eBay, Amazon or whoever else often sends you mail, are those messages found?)