The use of keep is both sentences is actually the same, and both are acceptable and commonly understood.
The first among the many meanings of keep is to maintain something in a particular state or condition. Whether or not a device is activated (i.e. on or off) can be one of those states, as in your first example, but you can supply any other adjective for the condition that is to be maintained:
Keep your laptop secure.
Keep your laptop updated.
Keep your laptop running.
In your second example, the participle charging indicates the state, so one could say
Keep your laptop charging overnight, to be ready to go in the morning.
Don't keep your laptop charging overnight, to save energy.
(As an aside, in my opinion it is slightly ambiguous to place to save energy at the end as a reader might interpret it as the purpose of "charging" instead of the purpose of "not keeping"; a comma makes the intent more clear by setting the infinitive phrase apart.)
