Why would scientific investigations lead to new investigations?

Answer 1

One reason is because the processes of science have no stages or components that assure beyond any possible doubt, past, present or in the future, that a given theory or 'law' is no longer falsifiable. Every investigation, even ones that support the tested theory, tell us something we didn't know before, and that something is falsifiable and therefore testable.

Another way of saying essentially the same thing is that even if the mathematics of a theory or 'law' is working in the operational sense, that doesn't mean that our conceptual understanding of the thing, based on the known math, is anywhere close to reality. More investigations based on our conceptual understanding or a new conceptual understanding may reveal something as yet unknown, or topple a long cherished belief.

Another aspect of the new investigations question is that once the basic theories of a thing are in place, there may be many details to fill in. The periodic chart is an example; once the orderliness of it became clear, it was no longer surprising or groundbreaking when elements were discovered that filled missing slots. That is not to say that this work is any less important, obviously. This is what Thomas Kuhn calls normal science.