The insurer has recently told me over the phone that my claim is being denied. What should I do?
Once again, see the advice given earlier to get it in writing. Immediately request that the denial be put in writing and demand (politely) that the insurer specifically tell you all reasons why the claim is being denied.
Most policies provide for an "appeal process" or "administrative review" (by the insurance company itself). While these appeals or reviews are frequently denied, be careful to comply with policy requirements concerning such appeals or requested reviews. Courts frequently reject a subsequent lawsuit where the insured has not "exhausted administrative remedies" (i.e., jumped through the policy hoops concerning the appeal process).