You can debug your extension's background.js
in the development environment (debugger) from the Chrome Extension page at chrome://extensions
:
It has a link to do that in each extension, often called "generated background page.html", (because Chrome generate a html page to contain your js).
If you're using Event Pages (background page with persistent:false in your manifest code), perhaps you should like to turn into persistent:true only for debug purpose.
The Event Page (i.e. persistent:false) unloads after few secondos of inactivity, and closes its debug window. persistent:true changes this, the page doesn't unload. It's better for debug, but turn into persistent:false when you get the debug done, because it's more efficient.