Why does my TwitPic upload cause a Network Request Failed error?

There is some problem using BIBS (or "BIS-B") to upload pictures to TwitPic.
Try changing your connection settings to use TCP or BES.

From inside TwitterBerry, click the "Configure" menu item. Change "Connection Mode" to BES if you are connected to a BlackBerry Enterprise Server, or TCP if you are not. Click "Test Connection" to connect to twitter.com to verify your connection. If a TCP connection is unsuccessful, make sure you have set the correct APN settings for your carrier.

To set your APN settings, go to the BlackBerry home screen, and choose the "Options" application. Go to Advanced Options, and then TCP. Input the APN, and username and password if appropriate for your carrier. You can find APN settings for a variety of carriers. Here are some places to start:
http://www.blackberryfaq.com/index.php/Carrier_specific_APN/TCP_settings
http://www.blackberryforums.com/blackberry-network/2185-blackberry-internet-msn-chat-web-telnet-tcpip-no-bes.html