The native iPhone IM software Apollo IM has been updated with new version, which is able to keep the program running even you are switching to other iPhone application.

The updates does not fix the problem entirely though, according to the developer,

The main problem with suspend is that the iPhone goes into a low power mode when shoved into your pocket waiting for a call - and this mode will shut off edge / wifi. Simply pinging the server won't keep the wifi up, as it seems the kernel does its best to plain unload it.

The team is now working on alternative solution, as well as implementing more IM supports using LibPurple.

Source [Apollo IM] via [myitablet]