This is for Rogers but it worked for Sprint as well.
From:crackberry Forums
Heres how to fix it.

1. Disable POP in Gmail
2. Enable IMAP in gmail
3. log into rogers.blackberry.com and delete your email account in the BIS
3. In your blackberry delete all the service books (Options > Advanced Options > Service Book >[Select each service book one by one, Press the Menu button and select "Delete", You will not be able to deleted the "Provisioning [PROVISIONING] service book]
4. Battery Pull (This removes the service books from the active memory) – Wait for the BB to load back up.
5. Log back into rogers.blackberry.com and recreate your email and filters (To prevent your sent items from coming back as new emails create a Filter that says: Do not send to device if From field is [your email address] – Press Save
6. Resend the service books to your BB through the rogers.blackberry.com BIS settings
(preform the steps in the order given)
You will get an email that says your email address has been set up.

Give it 20min to set everything up.

And your golden.

Please let me know how it goes.

Note: If you have POP and IMAP turned on in Gmail there will be a conflict issue and you will have speratic email dlievery, and you will only get 30% of your emails. See this thread for more details: Anyone having problems with Gmail, Push Email This will show some experiments i did which lead to me getting Gmail IMAP working properly.

***Also another another note, from some stuff i read, providers other than Rogers may not have PUSH IMAP.
Apparently Rogers and Google has some sort of deal in place that provides instant Push IMAP.

Please let me know if your not part of rogers and you can get PUSH (instant) IMAP from gmail and your service provider is not Rogers

In Regard to Email Reconciliation (Sync Deleted items and read items between BB and Gmail Server)
The steps provided above does not give you Email reconciliation with Gmail and BB.

Email Reconciliation:
To get Email Reconciliation working you need to have “Synchronize deleted items between this mailbox and my device.” checked in your rogers.blackberry.com Email BIS settings.

1. Log into rogers.blackberry.com
2. Press the edit button on the email account you want to reconcile with
3. Make sure the check box is checked that says “Synchronize deleted items between this mailbox and my device”
3. Press save

Settings for Blackberry Email Reconciliation as recommend by google (Settings to use on blackberry):
Delete On: Mailbox & Handheld
Wireless Reconcile: On
On Conflicts: Mailbox Wins

Also.

There is another way to set up your Gmail IMAP.
If you are using a new email that you have not used the BB before then continue. But if you want to fix your current email, and the above steps did not work. Try these steps. These are provided on the Gmail support site. They will actually give you more options in your BIS email settings:

You want to start from step 5, which takes place in the BIS at rogers.blackberry.com
Gmail Support – Blackberry IMAP settings

I tested the Google support way as well as my way and they both worked right away. But try my way as it seemed the steps I took seemed to make the BB email arrive faster (only by 20 to 60 seconds faster but still faster)