The tasks that apps can complete in the background are strictly limited to the following functions:
- Audio - continue playing audio with requiring the app to be in the foreground
- Location - provision of GPS data to background apps
- VOIP - Maintaining a connection fo Voice over IP applications
- Task Completion - Basically asking for a 10 minute (I'll stick with 10 during this answer, but it may be different) "pass" to stay running, ostensibly to complete a task like an upload or download, but often co-opted to just keep the app running for 10 minutes
Some included apps, but not 3rd party ones, have extended background capabilities for maintaining mail connnections, downloading into Newsstand etc, but these are not available to us mere mortals.
Strictly speaking it's true to say that apps can stay running for any purpose so long as they claim to be meeting the above limitations of use. Sometimes (I think the Sparrow email client tried this) an app can register as a VOIP service, even though it's not, thus enabling it to cheat the system and stay running at all time for some other purpose (in this case mail), but these apps are usually not successful in the review process, and even if they are are quickly pulled afterwards.
Basically, none of these capabilities will allow an RSS reader to regularly poll for updates whilst not being the active task. Most will implement the task completion service so any updates that come in within 10 minutes of leaving the app will continue to show etc, but after that you're out of luck.
Some apps (Instacast is one example) are quite clever about things, and at least combine the task completion capability with local notifications. When you leave the app, it will continue to download podcasts for 10 minutes. If they complete in this time, it will display a local notification, if not, they will register a 2nd local notification that will display saying downloads are paused to trigger when the 10 minutes is up, allowing you to quickly flip back in and out and grant it a further 10 minutes.