The ECoS is really a small computer system, which just like your PC don't like suddenly losing power. The batteries are there to provide power to allow it to shutdown cleanly and save your settings should power be lost without the system having been shut down first.
It is perfectly safe to take the batteries out once the system has shutdown and none of your settings will be lost.
As Pheaton says, the danger in not removing the batteries when storing the system for long periods is that the batteries could leak.
Alan