Hmm, well in that case I wonder if it's something with the helis, like maybe gear mesh set too tight or something. I don't really know what to tell you, sounds weird to me.

You shouldn't have to let them sit except maybe a few minutes to cool off a bit after flying, then go ahead and charge them up again.

You should always recharge them after flying them before flying again, don't fly them for a few minutes, unplug and let sit, then fly again without charging. I'm not sure about these helis, but some helis have a voltage sensor that will be off if you plug in a battery that isn't fully charged.