Why run it in the background and kill your battery life when BeejiveIM keeps you logged in as long as you like with push email notifications (including quasi text notifications using your phone's text email address) when you get messages outside of the app?
If you don't want to pony up the funds for that then you can use Palringo, which is free and I believe keeps you logged in up to an hour when you close the app, however it doesn't support notifications outside of what is supported with the IM protocols.
Even with just moderate chatting and closing BeejiveIM when I'm not chatting I find it really kills the battery life as does using any other application extensively does so I think Apple has a valid point in preventing apps running in the background, at least until they can reduce the power consumption of the operating system + apps on the iPhone.