Basil plants are annuals, meaning they go through their entire growth cycle in the span of a year, from seed to seedling to mature and flowering to seed-bearing to death. However, by trimming leaves, many gardeners prolong the useful life of the basil plant. The leaves are still spicy so long as the plant has not given over all of its energy to producing seeds. Some basil plants, even purple ones, can be kept alive in mild climates or in greenhouses for more than a year this way. Naturally, however, purple basil plants do not return from their roots after winter.
If the purple basil plant is fertilized by its pollinators (butterflies, moths, bees and other insects), the seeds will pop up the following spring. In a field or large stand of basil, it may seem as if the same basil plants have returned from winter dormancy, but the plants actually belong to the next generation.
To encourage purple basil plants to come back the following year from seed, you need to give them access to pollinators. You may hand-pollinate basil grown indoors, using a paint brush to move pollen from one flower to the next. Allow seed heads to remain on the basil plant until the seeds are mature. Then they can either be left to distribute themselves or harvested for later planting. The seeds need fertile ground that is not so overrun with other garden plants or weeds that the sun-loving seedlings cannot reach sunlight.
A purple basil plant whose life has been artificially lengthened by snipping off the flowers will usually grow woody at the base, and the vitality of the plant will decline over time. It will produce fewer leaves, and the leaves it produces may not be as vibrant, healthy or spicy. It will also likely be more attractive to pests that prey on weakened plants. After a certain point, it is better to allow the plant to go to seed and produce a young generation to add to your garden.