Have you changed your ISP or email hosting company recently? Have you spoken to either of these providers about the problem?
I’m on Windows 7 but imagine the mail client (Windows Mail Live) is basically the same. You could try installing another mail client – possibly Thunderbird (I think it’s win 8 compatible).
If your email account offers ‘webmail’ access, you could check to see if the ‘lost’ email(s) have actually been delivered to the mail server (account). If they haven’t then sounds like their may be a problem with the mail routing.
I’d check the server (webmail) fiirst, then depending on if they are there or not, speak to your mail hosting company and ask them to check the routing for you.