As long as you stay within its plastic deformation limit, "many cycles" should not matter.

PLA's downfall for flexible design elements is permanent deflection. It cannot be used on anything that is expected to stay in its tensioned state for anything more than a few seconds. This is why PLA works for catapults and toothpick guns and latches that have a single position rest state where the flexible element is relaxed. If you leave it under tension, though, even just for a few hours, it will not spring back fully. Eventually, it just won't spring back at all.

Through much testing (read: slowly pissing myself off) I determined in the course of developing my Rockhopper that ABS is the best commonly available choice for permanently or semi-permanently loaded printed spring fixtures -- at least out of what most normal and sane people can print with their hobby level machines. Even PETG is better than PLA in that respect, but PLA was useless for me.

I've Printed LOTS of PLA living hinges and even springs. They do work just fine for the limited to moderate cycles they last. I've printed 100's of toy catapults and other small toys in PLA and then handed them out to 8 and 9 year old children. They held up amazingly well under that abuse.