If you plan on putting your car in storage and taking insurance off of it, make sure to check with your state's Department of Motor Vehicles to see what you will need to do with them to comply with state laws. In many states you will need to turn in your registration and plates since the car is off the road and without insurance.
As for the insurance issues, you will likely lose some discounts, such as renewal discounts and without having an insurance provider for a few years or so some insurance companies may not choose to insure you. Some automobile insurance companies will not write you a policy without at least six months prior insurance.
Due to what the insurance companies will see as a gap in carrying auto insurance, your rates will likely be higher than what they are now when you first put an insurance policy back on the car and started driving it. If you do put your car in storage, when you decide to take it back out and need insurance, come to us for an affordable auto insurance quote with companies that will insure you even after a gap in insurance coverage.