Blackberry Internet Service can stop functioning for several reasons, usually for a simple reason, that can be fixed with a simple solution.
Useful Links - UK Network BIS Portals
Most Blackberry issues can be solved by pulling the battery while the device is on and replacing it after it about 10 seconds.
The Blackberry product can "fall" off your number at network level and needs to be re-provisioned by your network service provider. You can tell when this happens because GPRS/3G in the upper right corner is displayed in lowercase.
You need verify your e-mail on the Blackberry Portal. Every so often you need to do this, especially with hotmail/live accounts. Verifying your account can be done by logging into your Blackberry Account via the Portal and clicking on the red x.
Make sure your e-mail server is online & is sending out mail.
Sometimes Blackberry Desktop Manager can interfere with your Blackberry Service and this can be solved by uninstalling Blackberry Desktop Manager and reinstalling it, upon installation you will be prompted whether it is a Enterprise or Personal account. Closing the latter will re-enable your e-mail.