Inbox not picking up all emails

After someone said they had emailed me, and I couldn't see the email, I resent the email by clicking reply on my sent email, and their email response came up sitting before my response. But it could not be seen in the Inbox.

It happened again today, only this time I noticed I had received an email OK from the same person about a different subject. 

Other emails are coming through from other people and I haven't identified any other missing emails.