You can actually propagate this plant by leaf -plant it in a good sandy vermiculite soil, it will take 2-6 months. More certain is by division- make sure you have some good root. Don't repot until it's formed 2-3 leaves.
You can cut a piece of the plant down by the roots and then place it in water for a week or so till it grow roots. You need to cut the flowers off though and all but a few leaves.
You can actually propagate more violets from this one plant. This should be done in the spring time. Simply remove a healthy leaf including the stem (about 1 1/2 inches long) and place the stem in the container filled with soil that you wish to grow it in. Water well.