VirtualDub is a free video editor that allows to capture video. It works much better than Blackmagic Media Express.

VirtualDub settings for recording from xbox360 with Blackmagic Intensity Pro

• Use the same framerate that is used by xbox360 for outputting video
• Select "Capture" -> "Disk I/0" and set chunk in buffer to 64 and chunk size to 2 mb
• Select "Capture" -> "Timing" and check "Do not resync between audio and video stream" if you get audio and video out-of-sync
  You have some other things to configure like codec and you can capture the easy way.
  
• Select "Capture" -> "Hide display on capture" and hide your display to save PCI bandwidth.

If you still get dropped frames, you can try to capture uncompressed video. You can also disable audio:
Uncheck "Audio" -> "Enable audio capturing".
If you're still getting dropped frames with this settings then you may need to upgrade your CPU, memory or get a new computer.