You do not need to rewrite your entire website monthly. That would be a task no one would like to undertake. But with regular monitoring of your websites search performance, web logs and statistics will enable you to identify what your web visitors are looking for when they find you in their search results and allow you to make adjustments to your text accordingly.
Think about the websites you visit more than once a week. What draws you? Perhaps it is a daily blog or new photography. Perhaps it is that free download. The fact is, new, interesting and fresh content will bring visitors back to your site time after time. Nobody wants to read the same few paragraphs over and over! Keeping your site timely and current will not only increase traffic, it can also help your search engine placement.
A website should be updated as often as is reasonably possible and appropriate for your type of business. For an artist, monthly art and show updates may work. For a mail-order business, once a week or more often might be in order. Many informational sites and blogs are updated many times a day. Consider how often your target audience might consider your information useful when making the decision as to how often to update your site. And most importantly, stick with that decision firmly for as long as your website is needed.