I am a contractor involved in a construction defect lawsuit. My insurance companies have declined to defend. Timeline for appealing their decision?

This is a serious issue.  The carrier has a duty to defend the insured if there is any potential that the claimant could recover damages (any damages) that would be covered by the lawsuit.  Evidence outside of the complaint can be used by the insurance company, but it must eliminate the potential for coverage.  The supreme court has said that evidence that may tend to show that there is no coverage but do not eliminate it, is legally irrelevant. Many carriers today are using manuscripted policies, not industry standard forms, so there may be several reasons for non-coverage.  However, getting carriers involved early increases the chances of a settlement.   In answer to your specific questions, there is a school of thought that because the duty to defend is continuous, there is no duty to bring a lawsuit until 4 years (the statute of limitations for breach of contract) from the date that the case is resolved (and the defense costs stop). However, if you have been given a firm denial of coverage, I would be more conservative and use the date of the denial of coverage.  Also, in California, there is a claim that can be made for bad faith denial of coverage, which may have only a two year statute of limitations, though that question is currently open to debate whether it is 2 years or 4 years.  THEREFORE, to be safe, I would use 2 years from the date of the denial of coverage as the date you should either file a lawsuit or settle the action if plan to pursue it.