When the mounted Equis takes damage there is a chance that the taming progress will be reset.
Getting the Equis trapped in my quetzal's hit box gradually lowered the taming progress - this did not happen when it got stuck in wild creatures.
Once an Equus is spooked it tends to run forever and not allow it's self to be tamed.
You can ko the Equus for another passive tame attempt when it wakes up.
Equus seems to spook easily at night and spawn mostly during the day.