Here the answer:
Gmail uses Real-Time Delivery of Blackberry messages - push method.
And your new/current mail hosting service doesn't have that capability. It uses the common pull based delivery method to retrieve messages from your mailbox. That happens every 15 to 20 minutes.
As for today I am aware that Gmail, Yahoo, MSN Hotmail and AOL have implemented Real-Time Delivery for Blackberry.
So there is nothing you can do but to tell your email hosting provider to implement Blackberry's real-time delivery.
here is how it works (*)
REAL TIME DELIVERY OF EMAIL MESSAGES
1. A new email message arrives in a subscriber's email account from the Internet
2. The email account (GMAIL in this case) notifies Blackberry Internet Service (BIS) that a new email message has arrived
3. The BIS downloads the email message
4. The BIS sends the message to the subscriber's Blackberry device

The approximate delivery time is SECONDS.
Poll-Based delivery of email messages
1. A new email message arrives in a subscriber's email account from the Internet
2. The BIS checks the email account (mailbox) for new email messages every 15 minutes
3. When a new email message is discovered, the BIS downloads the email message.
4. The BIS sends the message to the subscriber's Blackberry device

The approximate delivery time is MINUTES
(*) The information comes from Feature and Technical Overview of the BIS ver 2.0 published by RIM