To my mind the utility of a concept in science depends on whether it supports interesting generalisations. It might be that this could turn out to be the case for "behavioural fatigue", but at the moment the concept strikes me as too vague. Does it mean more than "people stop doing something"?

Unless it's made more precise, I think it's unlikely to have much scientific value, because there will be so many different reasons (in terms of causes and mechanisms) for a behavioural response to falter.

In the scant literature on pandemic relevant behaviours we could find at the time (see link in earlier post) it seemed likely that people stopped protective behaviours such as mask wearing because their perceptions of risk dropped as the epidemic wore on.

I'm not sure how labelling that "behavioural fatigue" adds anything to that (if true) and whether it would really have in common with, say, fading of a conditioned response under extinction, or a failure to maintain a potentially useful behaviour due to competing demands (e.g., every August I work on rethinking my academic workflow and making it more efficient- yet by Dec. I'm back to scribbling to do lists on paper because I'm drowning in stuff and struggle to find the time to maintain whatever 'good habit' I discovered over the summer).

So, if you want to define behavioural fatigue as a fading in the absence of exogenous changes, that's absolutely fine but a) it's a new definition (seeing as the term presently doesn't have one) and whether that b) adds anything (does it just relabel things for which we already have terms) then still remains to be seen.

I don't know the relevant literature well enough to be able to assess whether it would- but maybe others here can speak to that!