iPhone - fast-app switching and iOS 4

I'm trying to get the following functionality in my iPhone app:

• When backgrounded, stays running (doesn't have to do any background work)
• When resumed, app picks up where it was left off

I'm mainly wanting the same screen on my app still up, as there are several UINavigationControllers within a UITabBarController.

I have done all of the following:

• Made sure I'm compiling with 4.1 SDK
• Set UIApplicationExitsOnSuspend to false
• Handle DidEnterBackground and WillEnterForeground in my AppDelegate
• Call BeginBackgroundTask in DidEnterBackground, to attempt to keep my app open

I'm using MonoTouch, but that it probably beside the point. I can take answers in Obj-C, for sure.

I've tested my app on a jailbroken phone with Backgrounder, and I see the "app in background" badge disappear immediately after pushing the home button. I also tried setting UIBackgroundModes in my Info.plist, but to no avail.

Is there anything I'm missing?

Or is this something I would have to implement on my own to resume the previous state of my app? Everywhere I've read talks like it should just work automatically.

I finally got in touch with someone on MonoTouch's irc.

In MonoDevelop there is an option to make a dual iPad/iPhone project, which I used. This is causing my app to behave as if it's running with the 3.2 SDK when deployed to the device.

I think my solution is to install the iOS 4.2 SDK that just came out, since this ads the new multi-tasking feature on iPad.