The general outlook mail settings will make the mails to disappear from the outlook inbox once after being read. In case, if you still need those emails in your inbox, then you have to enable the Leave a Copy of Messages On Server option in the outlook setting.
How to Leave a Copy of Email Messages on Server
A simple tutorial that explains you the procedure to leave a copy of email messages on server.
Step 1:Open Microsoft Outlook. Under Tools Menu, choose Email Accounts option.
Step 2: Click on More Settings.
Step 3: Click the Advanced tab. Enable the "Leave a Copy of Messages On Server" check box to prevent your email from being deleted after reading and click on Ok.
Step 4: Now, your mails will not be deleted from the webmail after reading.
Note: All the above given steps are for Outlook application to leave a copy of emails on the server. The procedure may vary for other applications.