Some contacts not displayed when searching for them
This can happen if you're using iCloud and it gets out of sync.  Go into Settings --&gt; iCloud and turn off Contacts.  It will ask if you want to delete the contacts on your iPhone or keep them.  Choose to delete them from your iPhone.

Exit iCloud then go back into it.  Turn Contacts back on and allow it to sync your contacts back to your iPhone.  If everything worked ok, you should be able to find that person in your contacts again.