It looks to me some strange pitfalls if you test your offline pages locally (not on webserver):
1. To test online/offline, you'd better enable/disable wireless/network card at the same time, especially when using wireless only. This affect both IE/FF. Possible message in IE: Sync error; Other console message: can not load firebug.js, dojo.js (not always, shifting when clicking). Some other error: UI name not defined...
2. These pitfalls may appear when you open 2 tabs of same content, or as mentioned in offline tutorial, when 2 pages share same offline database ( a known bug).
