This may be as a result or part of the moulting process, but can also be caused by other factors, such as stress, breeding, feather mites or another bird.
Stress can cause feathers to be shed, and it is difficult to diagnose. The best way is to observe over a long period and see if there is a particular occasion or action that causes the canary to fly in an uncontrolled way or hide in the corner of the cage. The solution is to remove the cause of the stress. I once had a lady that loved her new bird, which almost immediately started loosing feathers. She had a very large cat that loved sitting on the top of the cage watching the Canary. No the canary was not called Tweety.
When Breeding the hen often looses all the feathers on the abdomen down to the vent. This is nothing to worry about and the feathers will quickly return when breeding has finished.
Feather Mites. These usually donít cause baldness unless badly infested and usually just cause lines across the feathers. It can be treated with any one of the many mite sprays available from the pet supplier.
Another Bird. It often occurs with young birds; they start to pull the feathers of another bird. If this occurs separate the culprit. It can also sometimes be a parent wanting feathers to line a new nest.