You can try packing a little firmer, but are you sure you're getting the tobacco completely lit from the start? Make sure that you're covering the entire surface of the tobacco when you light up. Also, it sounds counterintuitive, but if you are puffing too much it can be harder to keep the pipe lit. You have to smoke a pipe slowly, especially a cob. This is where it becomes a real balancing act because if you smoke it too slowly, it won't stay lit. If it isn't lit from the start, you'll find it next to impossible to keep lit.
Keep working at it. If it doesn't work this time, change something up next time and see how that goes. Most people aren't going to pick up a pipe and start getting a great smoke straight away. IT takes patience, practice, and attention.