Usually, a life insurance company cannot cancel your existing policy unless you fail to pay the premiums, or lied on the application about your health or other material issue.
In addition, unless you have the option to renew on your term life insurance policy, you may be subject to a health exam in order to renew your coverage, and if they determine your health is bad, they probably will not offer you the option of buying another term life insurance policy.
For people who are unable to qualify for life insurance due to health issues, there are also guaranteed acceptance life insurance plans which may offer an alternative to going without life insurance.