Legal Question in Landlord & Tenant Law in California

Depends on several issues: terms of lease, origin/cause of termites. Generally speaking, yes, landlord is required to take steps to make the dwelling "Habitable" and if the termites affect "habitability" then you need to send a written notice and request they fix it.

The key word is "habitable." A termite infestation really only affects the structure, not the occupancy of the structure, until the structure is destablized in some way by the infestation. So until the termites have damaged the property enough to affect habitability, the owner or their agent technically is not obligated to do anything. On the other hand, extermination is ALWAYS cheaper than repairing the damage. So I can't imagine why they would want to wait.