Do they really quit? Or do they just switch off? I.e. iTunes stops playing, iChat disconnects etc.
Your title is a bit misleading, so I'll just explain the basics, and you'll have to correct me if this isn't what you meant.
You sound worried that the book 'sleeps' when you close the lid. This is normal behaviour for iBooks. They all sleep as soon as the lid is closed because a lot of the heat generated by the processor rises up through the keyboard area.
If they were left on whilst the lid was closed, the screen would be damaged and could even melt (there are pictures of that happening on the web somewhere).
So to protect the 'book, it goes to sleep, but will wake up instantly when you open the lid again.
All programs that were running will 'stop' any activity, but will remain open.