Yeah, why was he dying? Thought they couldn’t, hence a certain ep long ago of a Q wishing no longer to be.
The Q were unable to render themselves mortal or terminate their own existence - we know that. However, it was within the capabilities of the entire Continuum to unmake / remake a Q. Delancie's Q endowed Riker with some portion of the power of Q. In TNG's
Deja Q, Corbin Bernsen's Q gave Delancie's Q his powers back. In VOY's
Death Wish, Delancie's Q made Quinn mortal.
I always assumed these acts were more taxing than - say - morphing ol' Doc Crusher into a mutt. Both acts were done with the consent of The Continuum. You could assume it wasn't merely the Q present snapping their fingers, but the entire Continuum working through them. Otherwise, any Q could make another Q mortal and kill them. Although, The Continuum could resurrect the dead Q and would likely punish the offending Q for murdering a fellow Q. (Ugh - too many Q's).
Their natural immortality was baked in; they were billions of years old, as we reckon time. Then you have Q's "The Q didn't come into existence, the Q have always existed" line, implying they transcended our silly little notions of spacetime and cause / effect - which throws another wrench in the works.
So, we have some examples and some very Trekky inconsistencies. However, the changes made to The Q in
Picard directly contradict what had come before - that The Q do
not die by natural means. They don't ignore it, as per Guinan's reaction to Q's condition and statements re: Q killing other Q. The issue isn't the change itself, it's the absence of any attempt to explain said change.
Q muttered something about temporal horizons. That's all your giving us? The show ignores the rest of The Continuum, Q's family and the lore preceding
Picard and asks us to just go with it. I understand the thematic angle they were going for and not everything needs an explanation. In this instance, it was just rude. Worse, it was a red herring that had imaginations working overtime thinking something much bigger was going on than actually was. Q sick / dying, time broken, Picard the key to it all. If The Q are in jeopardy, there must be some serious multiversal shenanigans afoot! Nope.