The answer should be 180 days. The federal law, ERISA (short for Employee Retirment Income Security Act) that applies to most disability insurance benefits claims requires 180 days be allowed for a claimant to appeal the initial denial of their claim for disability insurance benefits.
The letter you get telling you that the insurance company has turned down your claim should tell you how long to you have to appeal the denial. It could be less than 180 days. If you're not sure what to do, contact an experienced disability benefits lawyer. You can reach Robert Abell at 859-254-7076.