Perennials should be divided when they are growing strongly and look healthy. Dividing a perennial when it is not going well will result in poor establishment. Also, some perennials will start to die out in the center of the mass. This is a sure sign it is time to divide.
WHEN CAN YOU DIVIDE PERENNIALS?
Most perennials can be divided in fall or spring. Mid-September is a wonderful time to divide. The soil is still warm enough for the roots to start re growing, thus giving the plant a great start in spring. Some plants such as Bleeding Hearts, Primroses, Anemone, and Monkshood prefer to be divided in spring. It is best to divide your perennials on a cool day. This will prevent the roots from drying out. If you cannot put the plants back in the soil right away it is a good idea to cover the roots with a bit of soil or wet newspaper.