No confirmed fix yet. Players suggest: if you have too many problems in the second competition you can enable auto-jump, but beware that your pace still has to be right!
Suggested fix (unconfirmed): Upgrade your stable so you have two or more groups of horses. Then, switch the horses between groups using the "manage" option for each horse.
Suggested fix (unconfirmed): Separate mares and stallions into different stable groups by using the "Manage" button or by clicking and dragging the horses. Alternatively, geld your stallions.