Is it possible to have a mobile web site that can still function if there's no internet connection?
The user should still be able to use the web site (if he has visited that page before), see the data (that was loaded before), add new stuff (cache locally). When internet connection comes back online, all changed local data should be pushed online.
This should be a complete web based solution, not a native app.
You should have a look at HTML5 offline storage, see http://diveintohtml5.ep.io/offline.html and the Offline Web Applications spec as a start. There are also quite a few posts here on SO.