Just to share, had them fall under me four times in 40+ years and 3 disciplines/breeds. By “Fall” I mean down on the ground off all 4 feet, not catching themselves with knees and nose staying upright, which you will see more and is less of an issue (unless they have perpetually skinned knees).
A 6 year old King bred QH, stout type, cantering across a hill got distracted by a pack of loose dogs chasing something. Took a misstep off the downhill side of the trail, legs followed downhill and he ended up on his side on the uphill side. Unfortunately he managed to land on an old telephone pole bordering the uphill side of the trail pinning my leg between his body and the pole. Some guy had to pull him around so he could scramble to his feet. I still have a dent in the side of my thigh.
4 year old Ayrab ( very fashionably bred) I was assigned to finish breaking at college. He’d just fall. Went flat twice in a couple of months in a sand ring. I asked some of the other students and was told ( yeah, he’s by XXXXX and they tend to do that more then the others). Never got hurt but asked to be reassigned and was told I was lucky to have a colt by XXXXX to work, if you don’t want him, you are out of the program. So I left. Had my own and any extra rides I had time for, all of whom could stay upright.
Last one was a 24 year old appendix, my third lease Hunter after I switched to Hunt Seat. Messing around in a lesson doing Jumper stuff. A 3 to a 3 to a 3 all verticals to an inside turn to a Swedish. Object was to balance after the 3s for the inside turn and find the center of that Swedish. Ground was wet, carried a goid bit of pace coming off that 3 , throttled back and swung into the turn, old guys back end just flew out from under him and down we went. Ended up driving self to ER but it was just a bad sprained ankle.
So…2 were freakish accidents but the other 2 with that colt by the sire du jour at the time? And they all hurt me so, no, I won’t deal with anything that has a history of falling for no reason, and even with reason if it happens more then once.