With normal use, contact lenses will stay firmly in position. Soft contact lenses are particularly stable, and are unlikely to dislodge, even doing active sports.
However, they can come out under certain conditions. High winds can cause the eyes to water and cause the lens to move more, increasing the chance of lens loss. A sharp blow to the head may dislodge rigid gas permeable lenses. And rubbing your eye carelessly may result in a lost lens.
Describe to your eye care practitioner all of the circumstances in which you are likely to wear your contact lenses. This will help him or her prescribe a type of lens that is less likely to be dislodged given your activities.