The time limit depends on state law. Generally, all claims must be settled within 24 months of the date of the accident. While most companies want to settle quickly, some will drag it out to avoid paying as long as possible.
The time limit is mentioned in your policy. you may contact your insurance department to find out additional details. And need to research your state's legal statues of limitations.
In every state, there is a statute of limitations for bringing or concluding a claim against the tortfeasor. Many states provide a two year statute from the loss date; others are one and three, respectively. However, these statutes can change based on circumstances and you should contact your states insurance commissioner for specifics to your case.