1. The other party's insurance company is still investigating liability.
Remember, just because the police report indicates their driver is at fault, there's still the chance their insured has told them a different story. Until that insurance company places liability on their insured, they will not extend you a rental. (The police report is not necessarily the definitive factor in regard to liability.)
2. You were struck by an uninsured driver and do not have a rental car provision in your policy.
Few people think to check their policy for rental car provisions. Some people believe full coverage automatically includes rental car coverage. Not true. I would suggest calling your agent to see if you have rental car coverage in your policy.
3. You were uninsured and placed at fault for the accident.