Synching with Gmail

I have GMail setup on my phone using the instructions found here
.
Setting Up Your iPhone or iPod Touch : Google Sync - Mobile Help

I couldn't figure out why messages were disappearing from my Inbox for the last little while but I was able to pinpoint the problem tonight. The issue is that I had sync setup to something like 3 days. After that, the messages were gone.

Now that I've got it up and running properly, is it possible to sync ALL OF MY MAIL. I don't like viewing my Gmail Inbox on my iPhone and seeing 4 messages when I know there are 400 messages in there!

Is there a way around this?

set it up as IMAP

Can you push IMAP?

yep
Official Gmail Blog: Push Gmail for iPhone and Windows Mobile

and if this wont do what you want there are more options:
http://www.google.com/search?client=safari&rls=en&q=can+you+push+with+gmail&ie=UTF-8&oe=UTF-8

My gf's primary email is gmail and she was frustrated with the lengthy delays in getting new mail sent to her 3GS. I found an app called Gmail Push that she now uses instead. New mail shows up instantly with nice push notifications when the screen is locked, plus the GUI is really nice. I believe it's either .99 or 1.99 well spent.