I've worked with a lot of people who will not engage with a request until the request has been made multiple times.

Its a very lazy way of filtering.

"It couldn't have been that important" is their logic.

I mentioned elsewhere that I was once coached to do this. In that situation it honestly wasn’t lazy at all. At the time I was fielding such a high load of incoming requests that even reading and responding to them was eating up a huge chunk of my time and preventing me from getting anything else (i.e., actually doing any of the requested work) done.

I realize that this looked to the people requesting my attention like deliberate stonewalling. That’s because it was. And it wasn’t cool. But, “This quarter I didn’t ship any software because I was too busy answering email,” would not have earned me a satisfactory performance review. And I certainly was not going to openly admit to anyone but my immediate manager that I was using persistence as a prioritization signal. I saw what happened to the poor schmuck who made that mistake.

What I learned managing high performers is a disproportionate number of them had very hard childhoods and carry permanent scars that make this behavior destructive. These are the people that generally get ignored in every aspect of their life because their brain is operating much faster than the rest of society and get mistaken for being insane in every facet of their life. So when they experience this kind of behavior in an environment that's supposed to reward them for their ideas, it's stultifying. Those high performers are not going to continue putting effort and energy into novel ideas if they're being ignored.

The solution is pretty simple: just fire the manager.