The horses become very confused because the signals are all mixed up. My horses are used to being ridden with soft, pliable leg contact which only changes briefly to give signals and then softens again. If you are tightening your legs when the horse trots you could be causing the horse to think you want it to stop. Make sure you keep your balance, hold your hands and arms really steady so they don't jerk the horse in the mouth, and keep your leg muscles relaxed without flapping. You must also maintain an enthusiastic attitude and you must really be keen on continuing trotting, without getting uptight or frustrated.
Horses feel the tension in the rider and become anxious themselves and then get even more confused.
The crop or whip should be used to say listen to my legs. It should be your legs that nudge the horse into the trot and remind it to keep going when necessary. We need to give them the benefit of the doubt, give the horse time to respond to the first and second requests and if they don't then wake them up or get their attention with the whip. Use of the whip as punishment for bad manners or kicking other horses is a different subject.