First of all, it all depends on the TYPE of insurance you are taking out.
If you are buying annual renewable term, in which the premium increases every year, or every 5 years, the company may well allow it -- but to be sure demand the agent give you a letter in writing to that effect signed by an officer of the company on the insurance company's letterhead. (Apart from the fact that policies always say that only an authorized officer of the company can vary the terms and conditions, and its agents have no authority -- which may or may not be the case -- the agent likely would not be around or working for the company in X years -- at some companies the half-life of an agent is as short as a year.....
The company is not bound to do anything that the policy does not specifically allow. But let's face it. If you were in bad health you'd want to keep the policy at full face value anyway, and if you were in excellent health you could always drop it and take out new insurance, so it's no big deal. And in any event you can bet the agent will be back to try to have you "convert" the policy to a form of permanent cash value (whole life, universal life or variable life) insurance in several years or at least tell you to drop this policy as there "is now a cheaper and/or better form of term life". (Certainly the agent will do so if s/he leaves the employ of his/her current firm, because that's how agents earn commissions!)
One of the most popular forms of life insurance today, and the least expensive, is 10 or 20 year term life. Why? The insurance company underwrites you today and based on that favorable assessment of your health, can provide a very good rate if your health is above average and you have no real risk factors. (The ill, or those in danger of health problems, pay a higher rate, often VERY much higher.) In time the effect of that selection process wears off, and in 10 to 20 years your health is no better than the average for your then attained age.
With 10 or 20 year term the company takes on the risk for a limited period only. 10 or 20 years from now the policy is OVER. Period. You have to apply for a NEW policy, and if you qualify, you'd get a good rate then, Of course if your health has declined, you won't get a good rate, assuming you could buy any insurance at all.
Sometimes 10 and 20 year term policies give you a right to convert the policy to (a far more expensive form of) permanent insurance that you can keep long term, but conversion rights usually expire several years before the term policy itself lapses. (The fact is that the sick are FAR more likley to convert than the healthy, who could easily buy a new policy. And thus conversions are costly to the companies. As those who are ill usually only start looking at the end of the term, the company does not want the burden of the increased mortality risk they bring with them. So this way it has its cake and eats it too, as the policy has a conversion privilege, but most folks who would take advantage of it are likely to let it slip away.)
