Children can easily get lost when they wander off the trail or get out of sight of an adult.
You can avoid losing a child by always staying in visual contact of one another. Don't let children run off too far ahead, lag behind, or go off trail (that's why it's generally not advisable to play Hide and Seek on the trail). Children who set the pace in the lead should stop whenever they turn around and can't see an adult (and they should turn around regularly).
Teach kids to stay on the trail by learning how to follow the path: recognizing blazes, rock cairns, visual clues like logs, brush piles blocking reroutes, and so on. You also can use the buddy system. One child likely will encourage the other to not wander off, and if he doesn't at least they won't be lost alone, which can be far more frightening and dangerous.
When a child realizes he's lost, he should stop, remain where he is, stay on the trail, and blow the safety whistle three times. This will help you identify your child's location sooner. Also, teach children the importance of not crying wolf. They should use the whistle only if they really are lost.
Lost children who see other hikers should tell them so. The adult hikers may know your whereabouts and be able to bring the child back to you. At the very least, the child is in care of an adult rather than alone. In this day and age, there always is fear that a stranger may be a dangerous weirdo, but on a remote trail traversed only by hikers, the odds really are against it.
Unless there are recent reports of a kidnapper or molester on the trail (in which case, you ought not to be on it anyway), the child shouldn't pass on the opportunity of receiving help as another adult might not be along for a very long time.
Likewise, children should be told that they need to answer the calls of their searchers. Some young children will not respond because they think they shouldn't talk to strangers or because they're afraid they'll be in trouble when found.
Read more about day hiking with children in the guidebook Hikes with Tykes.