3DS does not multitask. If you quit FBI (or even, I suspect, press the Home button) then it will interrupt the installation of the CIAs. This is dangerous, as a half-installed CIA could cause a brick (depending on what it is), or mess up the ticket database.
When you're doing something like installing a CIA, you should really just leave your 3DS alone until it's finished.
Edit - and plug the charger in before you start installing.