cadence slows when tiring?

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I normally spin a pretty fast cadence...90-100 on flats and 85-90 on climbs. This is comfortable for me and doesn't tire out my legs as much. I am also a tiny rider, 5'4" 117 lbs. so this cadence range fits me well.

However, when I start getting tired, like really tired (ie. races like a time trial or a hilly RR), I find myself pushing not necessarily a bigger gear but a slower cadence...like 70-80 on climbs and 85-95 on flats. My muscles are definitely hurting but I find it that during these moments, when I switch to a lower gear and try to spin faster (back in my comfort range) I slow down (and it hurts too!). So, I end up spinning a lower cadence, just grinding it out, muscles aching and breathing hard as well but going faster than if I were in a lower gear spinning faster.

So, do I need to rethink my comfort cadence range or what? Why is it that I can go faster pushing a larger gear/slower cadence when I am very tired vs. spinning in my normal cadence range?

Thanks.