As stated by the dev, ABP needs to have a notification up constantly in order to avoid being killed. However, in Jellybean, this is no longer a problem! If you go into Settings -> Apps -> Downloaded -> ABP there is an option to Tick/Untick "show notifications". Simply untick it and you're good to go. ABP still technically has a notification active which stops it being killed, but Android is just not displaying it.
Sorted.