Q: "My insurer is supposed to take my monthly payment out of my checking account, but didn't do it for three months. Now they want me to pay for three months all at once. Can they do that?"
A: Sorry to tell you, but the short answer is yes, since they provided coverage for those three months. But since they erred by not taking the payments on time, it's worth asking if they'll allow you to pay in installments, so you don't get hit with a triple bill all at once.
When you know that a monthly insurance premium is supposed to come out of your bank account and you notice that it doesn't, don't wait and hope that that means you get free insurance. Call your agent or insurer and find out what's going on.