Establishing a solid negative result that rules out hypotheses is worthwhile if unglamorous.
Citing an upper bound on the half-life is all that can be credibly reported. It's how you put an error bar on something that's non-negative but consistent with zero.
The life sciences equivalent would be a study of unicorn sightings. None so far, but they could be put there so please fund my research!
Whether to fund difficult research, when it's reasonable to give up, and when it escapes beyond reasonable definitions of science, are separate questions. Physics is wrestling with these questions in a number of areas, such as the search for an empirically testable theory that reconciles quantum mechanics and gravity.
The life sciences have no equivalent. Precision measurement is not their bag, which is OK. Physics is the first to arrive at such a roadblock. Maybe the search for proofs of some famous math conjectures is an analogy to draw guidance from.
It's fascinating that someone can make a career out of a phenomenon not being observed.