>>724082889
Basically uma has hp. When late race begins your uma checks their hp. If they have enough hp left to do it they immediately begin last spurt aka attempt to accelerate to their max speed and will run at max speed until the race ends. If they don't have enough hp they will delay this acceleration phase until either there's enough hp left to run the rest of the race at max speed OR the actual "last spurt" phase begins. This last spurt phase is the last few hundred meters of the race and at this point all umas will accelerate to max speed with no consideration for stamina, usually then running out of hp and hitting a massive speed penalty.
The issue is that this critical "do I have enough hp to immediately switch to max speed mode"-calculation is only done once at the start of late race. So any stamina you recover after this doesn't help you get to this mode, it just helps you combat debuffs.
Here's an example from the simulator. See when middle leg ends the red horse shoots up in speed (instant max speed attempt) while the blue just falters around, only starting the big speed up much later and then completely dropping speed once it runs out of hp on the forced last spurt.