This so called "missing refreshes when you sleep" doesn't reduce your chance to get 6*.
By your logic if I don't check shop for month - my chances of getting 6* on next refresh should be zero, because I missed so many refreshes.
But it's not zero, it's same 3% as always was.
In case of independent tries only thing that matter is number of tries. And with system like "ON\OFF switch" number of tries will be lower (or same if you manually refresh every 3 hours) in comparison to automated refreshes.