My agent tells me I cannot cancel the term insurance policy I just purchased or I will never be eligible for insurance again. Is this true?

First of all, a policyholder can cancel his policy at any time even after several years into the contract. However, if your health has deteriorated and you need insurance, it might not be advisable to cancel your policy unless you make sure you have preferable replacement coverage in place. If your health has declined drastically, you might indeed not be able to qualify again or the cost of insurance might be prohibitive.