Some external circumstances could change reducing them to a pile of oxides, but the systems themselves were perfectly self-perpetuating -- i.e. time-independent, or put another way 'given enough time' is not sufficient.
Of course, before the heat-death of the universe entropy-reducing systems will break down, but that's not an interesting observation.
> Some physical processes decrease entropy locally, sometimes by incredible amounts.
I think that's the more interesting observation. How to qualify life beyond only 'local entropy reduction systems'.
My uninformed opinion is that it is both 'entropy-reducing' and 'context-dependent' systems that should be considered 'alive' (not sure though that this is sufficient). Dependence on their context means that those systems will have a feedback-loop with their environment, allowing for example non-linear causality and thus complexity to emerge.
A star radiating away their stored negative entropy is an all give and no take, no dependency, full autonomy system. Of course they can still be impacted by external effects, but sustaining their own internal processes does not require such inputs, they are incidental to them emitting away their stored energy. Once started, their schedule (when they will deplete themselves, collapse, etc) is known and predictable, thus not alive.