Outlook does not leave mail on server

[metal_cd]

I have the option in Outlook selected to leave e-mail on the server, but it
still seems to be downloading the e-mails, because e-mails that I do receive
through outlook are not available on the webmail site.

Also, I'm wondering if forwarding causes messages to not be delivered to the
normal mailbox, hence not showing up in outlook.
Thank you

[cPanelDavidG]

I have the option in Outlook selected to leave e-mail on the server, but it
still seems to be downloading the e-mails, because e-mails that I do receive
through outlook are not available on the webmail site.

Also, I'm wondering if forwarding causes messages to not be delivered to the
normal mailbox, hence not showing up in outlook.
Thank you

Forwarding does not cause issues with messages being delivered to the normal mailbox.

Have you tried using IMAP instead of POP3 in Outlook? IMAP is specifically designed for being able to access mail on multiple machines by means of keeping mail on the server until you delete the message. POP3 with the option of leaving messages on the server is a bit of a kludgey attempt at replicating this functionality IMAP provides.