I'm always charging my iPhone 4s and 3gs while apps are running on the background, wondering if it can degrade the battery's lifespan.
Yes, if u always charging phone while apps are runing on background will degrade the battery's lifespan
Apart from navigation and music playing, background apps aren't really running Even if they are, it has nothing to do with charging.
You should let the battery run down occasionally (every month or so) to calibrate the battery indicator, but otherwise, charge as convenient to you.
Retrieving data ...