From Greg Truty:
I think you really mean offline support and not session persistence since session persistence requires connectivity. That said, HTML5 offers offline support via a local store using named value pairs. As HTML5 is being developed, there are a couple of other standards that have been defined: web SQL storage and indexed databases which are Apis to a local store in the browser. The answer here isn't as clear as the initial WHATWG defined web SQL storage, but as it went through the W3C, they deprecated it and are pushing for indexed db. Most of the customers we see wanting to persist some data use this, however due to some enterprise concerns that the device could be lost and data released, we see many applications keeping little to no data on the device from a pure mobile web solution.