Emails Suddenly Disappearing
There can be several reasons for why your emails seem to have suddenly disappeared.
It is possible someone logged in and deleted or moved the emails. Check your other folders, especially Spam and Trash.
POP Access Used
If you made a POP3 connection via Outlook or another mail client, then the emails may have been moved to the computer which made the POP3 connection. Check the Outlook or other mail client on that computer.
To prevent this from happening, be sure to set your POP3 account to leave copies of messages on your server. In Outlook, this is found at Tools > Accounts > Edit the email account > More Settings > Advanced > check box for Leave a copy of messages on the server.
Accessing the Wrong Account
This mistake is much more common than you think. Be sure you are using your full email address for the user name when you login. If you put your cPanel username, you will be in the wrong place.
Again, the user name you login with must be an entire email address, like email@example.com. If you are not putting the @example.com part, then you will not see the correct inbox.
Third Party Scripts
Some scripts by default use POP3 to retrieve emails from the server. It is recommended to use IMAP for retrieving your your emails. You will need to consult your developer regarding the setup and/or configuration of said script(s).