Term life insurance is unique in the sense that, at the end of the term, the underwriters can re-assess the risks of the particular insured. At the end of the term, sometimes rates go up, down, stay the same, or sometimes coverage is cancelled. Health and age may be two factors they look at, depending on your situation. As some of the other attorneys pointed out, however, no concrete answer can be provided without reviewing the terms of the particular policy.
It depends on the policy's provisions and applicable laws. No one can answer your question except to say "Maybe."
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I agree, it depends on the wording of the policy. Generally speaking, most term life insurance policies cannot be cancelled by the insurance company for health reasons.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.