If the problem is in relation to a claim, you may be limited to a period of 90 days to correct any problems with the claim and make it acceptable to the insurance company. If you do not meet the requirements of the insurance company during that period you can file for an extension. Similarly, if the case has been denied and is now being considered for legal court, the claim will remain open until a legal ruling has been made on the case.
If the problem is in regards to getting a home insurance policy, the length of time you have to fix any problems is up to the insurance company. For example, if your insurance is being held up due to limbs hanging dangerously over the house you may have a 30 day grace period during which your insurance will be effective be will not include any damage caused by the offending limbs or branches. If the house is deemed uninsurable, you may not be able to correct the problems no matter how much time is available.
Keep in mind that homeowners insurance may be a condition of your mortgage. If this is the case, you need to get the problems sorted out as soon as possible to prevent fines or a rejection of your mortgage. If this scenario, the insurance company is not the agency you need to worry about, but the lender. If you do not follow the conditions of your mortgage you can be considered to be in breach of contract and the lender has the option of demanding the entire outstanding mortgage balance. This very rarely happens, but it is a possible scenario. What is more likely to happen is that the insurance company will secure a policy on the home and apply those charges to your monthly mortgage, usually after a markup.