A Canary doesn’t sing during the moulting season. This usually happens during the summer, and lasts from 6 to 8 weeks (anything longer, or involving bald patches, is probably down to disease – see Finch Diseases, below).
Canaries only start to sing after about 12 weeks, so a mute bird may simply be a young one.
Females are not, generally speaking, great singers, so if you have a reluctant performer, it may be a hen. However, many owners have trained their hens to sing very well. They can’t master the more intricate rolls and warbles, but they can still become good singers.
Silence isn't golden - but there will be a good reason why your Canary isn't singing
Canaries need stimulation if they are to reach peak song performance. Sound and movement help, so the bird should be kept in a room with a decent amount of family activity taking place beyond the cage. If the Canary is part of an aviary, the other birds will provide the stimulus.
Only a healthy bird will be inclined to sing. If your Canary is silent, but is in none of the categories listed above, he could be sick. Check that his diet is top-notch, and do a spot-check of his appearance, cage and immediate environment (e.g. is he fluffed up or sleepy, or suffering from the incursions of draughts, pets, small children, other birds, etc).