Until such a time as their illegitimacy is demonstrated.
Which, by the way, is exactly what we are striving to do.
Should he be proven to have never been qualified in the first place, this would arguably nullify every law he's signed and every appointment he's made.
Don't know about you, but that would be worth it to me!
You might argue it, but you'd lose - decisively. From Ryder v. United States...
"The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that persons appointment or election to office is deficient"
Other decisions reaffirming or citing this principle include, but are not limited to Norton v. Shelby County (where it was initially established)The People of the State of Colorado v. Adolph Quinten Sherrod.
This is not a complicated question of law. Precedent is well-established and is reinforced under the principle of stare decisis.