She refused because her name had to be on the licenses. When the new law removed that requirement the deputies could issue the licenses.
Let's keep the facts straight here. Deputies were issuing licenses well before any change in the law to allow removing her name. There was only a brief period were her refusal had any effect on the public. My understanding was that the clerks were issuing licenses without her name on them despite the fact that the law required her name on the certificate. Kim Davis was ordered not to interfere.
Later, a law was passed to clear up the idea that the certificates were not valid and of course to protect the clerks like Kim Davis.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
History will have to record that the greatest tragedy of this period of social transition was not the strident clamor of the bad people, but the appalling silence of the good people. Martin Luther King
I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend. Thomas Jefferson