AbiWord will exit when you click on Close if you have just one document open. If you have two or more documents open, when you Close the one that you're working on, the other document will then be visible and AbiWord will not close. At least that's how it works for me.
If you want to open another document, while the first document is on screen, just go ahead and do File, Open. You should now have two documents showing under the Documents menu. If you close one, AbiWord will stay open with the other document on screen.