Is there a way to force an app to remain running in the background no matter what?
The accepted answer turned out incorrect or outdated. The "App Settings" module for the Xposed app allows you to specify on a per app basis to keep apps from being killed or freed:

http://repo.xposed.info/module/de.robv.android.xposed.installer

http://repo.xposed.info/module/de.robv.android.xposed.mods.appsettings

Responsible care should of course be exercised when playing with apps changing such low level behaviour.