Keep in mind that “cost” means something slightly different here.
Normal functional costs of government operations are accounted for, budgeted, and paid out either by revenue or debt. It is the “cost” of doing government business. Paying employees, funding projects, moving liquid assets around to banks, paying off our debts and bonds, stuff like that.
Again, these are planned expenditures
Shutdown costs are different. Shutdowns lead to unexpected and unaccounted expenditures on top of what the government already has to spend. Most of this comes out of slush funds.
The biggest drain, however, is that shutdowns choke revenue. Which means that expenditures that were already budgeted in suddenly may become a victim of a shortfall. This revenue is not easily recouped, because the cost of doing government business continues even when the government is shutdown.
An example. There are around 144,000+ government employees. Of those, around 110,000 (myself included) work jobs that require network access. This access is accomplished through something called a PIV or CAC card. Each card is tied to a credential that grants access to the network of your department.
These credentials cost 10 dollars a day to maintain.
Some quick and dirty maths and you get 1.1million dollars a day to keep those cards online. The PIV system has a static budget that is outlined at the start of each fiscal year. Revenue disruptions mean shortfalls.