Making iPhone Web Apps continue to run after they went offline used to be an uphill struggle. However, with the specification of up-and-coming HTML5, you can now load a web app just once and then let it run offline. All this, without a need for a continuous internet connection, giving it the feel of a locally installed native iPhone app.
In his recent post on Mobiforge, Wei-Meng Lee explains how to use Dashcode to write offline iPhone web apps. His article gives you a great step-by-step explanation, from the Configuration of Apache for Web Publishing to Session- and Client-side Storage.
If you are about to develop an app with offline mode, I recommend you read through Wei-Meng's article for further insights. You can find it by clicking here.