A person's exclusive rights granted under U.S. statutory copyright law do not expire when the person ceases to promote the work.
The Copyright Clause of the Constitution does not provide copyright protection. It grants a power to Congress to create laws with a particular purpose. The Supreme Court has analyzed Congress's exercise of this power under a rational basis standard: are the laws chosen by Congress rationally connected to the specified purpose of the granted power (i.e. the promotion of science and useful arts)? See e.g. Golan v. Holder, 566 U.S. 302 (2012).
The Court has not required the laws created by Congress under this power to be so narrowly tailored such that they would only grant rights in circumstances where the rights actually promote the progress of science and the useful arts in that particular case.