torchy is correct... You need to set your phone to "leave a copy of mail on the server".... I use a Palm Treo 700p (read: not a sidekick) to retrieve my gmail... So I'll describe in non-exact terms what you need to do, and I'm sure you'll get it set-up correctly (the way you are wanting it) on your sidekick.
Go into your email program on the side kick... Edit accounts... leave everything as it is, except find a section marked "more" or "advanced"... look through it (normally in a section called "servers") and find something that says "leave a copy of message on the server"... you need to ENABLE that feature....
Also... you will probably want to do the same within the Mail application on your Mac.
Having these set-up as-so, will ensure that EVERY e-mail that is sent to you will be received by your Gmail online account, your Mail.app on your Mac, and your Sidekick...
Let us know if you need any help.